The following reports contain the obtained results during the period 2011-2016 (splitted into sub-periods):
Report 2011-2013: [pdf];
Report 2013-2014: [pdf];
Report 2014-2015: [pdf];
Final Report (including the period 2015-2016): [pdf];
Objectives:
C2.I. Wulff symmetries in anisotropic elliptic problems
C2.I.1. Quantitative anisotropic isoperimetric inequalities
C2.I.2. Anisotropic Hardy-Rellich inequalities
C2.I.3. Wulff shape minimizers in integral inequalities
C2.II. Principle of symmetric criticality in non-euclidean structures
C2.II.1. Symmetries of anisotropic medium
C2.II.2. Symmetries in Riemannian manifolds
C2.II.3. Symmetries in Heisenberg groups
A. Kristály, D. Repovs, Quantitative Rellich Inequalities on Finsler-Hadamard Manifolds, Communications in Contemporary Mathematics, Volume 18 (2016), Issue 6, 1650020 (17 pages), AIS: 1.599; impact factor: 1.167 [pdf]. C2.I.2
Cs. Farkas, A. Kristály, Schrödinger-Maxwell systems on non-compact Riemannian manifolds, Nonlinear Analysis: Real World Applications, Volume 31 (2016), 473-491, AIS: 1.311; impact factor: 2.237 [pdf]. C2.II.2
A. Kristály, Gagliardo-Nirenberg inequality and its limit cases on metric measure spaces: volume growths and rigidities, Calculus of Variations and PDE, Volume 55:112 (2016), AIS: 2.929; impact factor: 1.555 [pdf]. C2.I.1, C2.I.3
Z. Balogh, A. Kristály, K. Sipos, Geodesic interpolation inequalities on Heisenberg groups, C. R. Math. Acad. Sci. Paris, Volume 354 (2016), Issue 9, 916–919, AIS: 0.890; impact factor: 0.446 [pdf]. C2.II.3
I. Mezei, A. E. Molnár, Schwarz symmetric solutions for a quasilinear eigenvalue problem, Electronic Journal of Qualitative Theory of Differential Equations, Volume 89 (2016), 1-17, AIS: 0.408; impact factor: 0.732 [pdf]. C2.II.1
N. Costea, M. Csirik, Cs. Varga, Linking-type results in nonsmooth critical point theory and applications, accepted, August 2016. Doi: 10.1007/s11228-016-0383-6. Set-Valued and Variational Analysis, AIS: 1.502; impact factor: 0.973 [pdf]. C2.I.3
R. Precup, P. Pucci, Cs. Varga, A three critical point result in a bounded domain of a Banach space and applications, accepted, August 2016. Differential and Integral Equations, AIS: 1.376; impact factor: 0.851 [pdf]. C2.II.1
A. Kristály
Talks:
1. University of Santiago de Compostela, Santiago de Compostela, Spain, 7 September 2016.
Title of the talk: Gagliardo-Nirenberg inequalities on metric measure spaces: volume non-collapsing and rigidities.
2. Conferinţa „Diaspora în Cercetarea Ştiinţifică şi Învăţământul Superior din România-Diaspora şi prietenii săi”, Workshop: Sisteme dinamice. Teorie şi aplicaţii Timisoara, Romania, 26-27 April 2016. [link]
Title of talk: Geometric inequalities on metric measure spaces: volume growths and rigidities.
Scientific Collaboration:
1. University of Santiago de Compostela, Santiago de Compostela, Spain, 6-12 September 2016 (prof. A. Cabada).
Cs. Varga
Talks:
1. Workshop Geometry and PDEs, West University, Timișoara, Romania, 10-11 June 2016. Invited Speaker [link]
Title of the talk: Singular Poisson equations on Finsler-Hadamard Manifolds.
Scientific Collaboration:
1. Eötvös Loránd University, Budapest, Hungary, 1-7 May 2016.
Cs. Farkas
Scientific Collaboration:
1. University of Santiago de Compostela, Santiago de Compostela, Spain, 6-12 September 2016 (prof. A. Cabada).
2. Universita di Catania, Catania, Italy, 25 July 2016-2 August 2016 (prof F. Faraci).
I. Mezei
Scientific Collaboration:
1. Universita di Catania, Catania, Italy, 25 July 2016-2 August 2016 (prof F. Faraci).
Cs. Farkas, A. Kristály, Cs. Varga, Singular Poisson equations on Finsler-Hadamard manifolds, Calculus of Variations and PDE, Volume 54 (2015), Issue 2, 1219-1241, AIS: 2.929; impact factor: 1.555 [pdf]. C2.I.2, C2.I.3, C2.II.2
Z. Balogh, A. Calogero, A. Kristály, Sharp comparison and Aleksandrov-type maximum principles in Heisenberg groups, Journal of Functional Analysis, Volume 26 (2015), Issue 9, 2669-2708, AIS: 2.474; impact factor: 1.273 [pdf]. C2.II.3
F. Faraci, Cs. Farkas, New conditions for the existence of infinitely many solutions for a quasilinear problem, Proceedings of the Edinburgh Mathematical Society, Volume 59 (2016), 655–669, AIS: 1.181; impact factor: 0.73 [pdf]. C2.II.1
R. Filipucci, P. Pucci, Cs. Varga, Symmetry and multiple solutions for certain quasilinear elliptic equations, Advances in Differential Equations, Volume 20 (2015), Issue 7-8, 601-634, AIS: 1.543; impact factor: 0.917 [pdf]. C2.II.1
M. Mihailescu, D. Stancu-Dumitru, Cs. Varga, On the spectrum of a Baouendi-Grushin type operator: an Orlicz-Sobolev space setting approach, Nonlinear Differential Equations and Applications (NoDEA), Volume 22 (2015), Issue 5, 1067-1087, AIS: 1.313; impact factor: 0.796 [pdf]. C2.I.3
H. Lisei, R. Precup, Cs. Varga, A Schechter type critical point result in annular conical domains of a Banach space and applications, Discrete and Continuous Dynamic Systems, Volume 36 (2016) Issue 7, 3775-3789, AIS:1.626; impact factor: 1.127. [pdf] C2.I.3, C2.II.1
A. Kristály
Talks:
1. MAnET Workshop on Sub-Riemannian Analysis, PDE and Applications, Bern, Switzerland, 26-30 January 2015. Invited speaker. [link]
Title of talk: Functional inequalities on metric measure spaces with applications.
2. Workshop "Advances in Game Theory", Reggio Calabria, Italy, 7 May 2015. Invited speaker. [link]
Title of talk: Geometric aspects of Nash equilibria: the influence of the curvature.
3. The Eighth Congress of Romanian Mathematicians, Iasi, Romania, 26 June-1 July 2015. Invited speaker. [link]
Title of talk: Gagliardo-Nirenberg inequalities on manifolds: the influence of the curvature.
4. ICNODEA (International Conference on Nonlinear Operators, Differential Equations and Applications), Cluj-Napoca Romania, 14-17 July 2015. Invited speaker. [link]
Title of talk: Poisson equations on Finsler-Hadamard manifolds.
5. 5th MATINFO International Conference, 2015 September 2–5, Sapientia Hungarian University of Transylvania, Tg. Mureş, Romania. [link]
Title of talk: Interpolation inequalities on manifolds: from best constants to rigidities.
6. Central European University of Budapest, 14th September 2015,
Title of the talk: Geometric information encoded in best Sobolev constants
Scientific collaborations:
1. City University of Hong Kong, Hong Kong, China, 1-31 March 2015 (prof. Ph. G. Ciarlet).
2. Universita di Catania, Catania, Italy, 19-30 August 2015 (prof F. Faraci).
3. Universitat Bern, Bern, Switzerland, 11-31 October 2015 (prof. Z. Balogh).
Cs. Varga
Talks:
1. Eötvös Loránd University, Budapest, Hungary, 27 April 2015. [link]
Title of talk: A Schechter type critical point result in annular conical domains of a Banach space and applications.
2. The Eighth Congress of Romanian Mathematicians, Iasi, Romania, 26 June-1 July 2015. Invited speaker.[link]
Title of talk: Symmetry and multiple solutions for certain quasilinear elliptic equations.
3. ICNODEA (International Conference on Nonlinear Operators, Differential Equations and Applications), Cluj-Napoca Romania, 14-17 July 2015.[link]
Title of talk: A Schechter type critical point result in annular conical domains of a Banach space and applications.
4. Eötvös Loránd University, Budapest, Hungary, 14 September 2015.[link]
Title of talk: Localization of positive critical points in Banach spaces and applications.
5. University of Pécs, Pécs, Hungary, November 2015.
Title of talk: Location results in critical point theory and applications.
Scientific Collaboration:
1. University of Pécs, Pécs, Hungary, 2-6 November 2015.
Cs. Farkas
Talks:
1. ICNODEA (International Conference on Nonlinear Operators, Differential Equations and Applications), Cluj-Napoca Romania, 14-17 July 2015.[link]
Title of talk: A quasilinear elliptic problem involving critical Sobolev exponents.
2. 5th MATINFO International Conference, 2–5 September 2015 , Sapientia Hungarian University of Transylvania, Tg. Mureş, Romania.[link]
Title of talk: Singular Poisson equations on Finsler-Hadamard manifolds.
3. Universita di Catania, Catania, Italy, October 2015.
Title of talk: Elliptic equations on Finsler manifolds.
Scientific Collaboration:
1. Universita di Catania, Catania, Italy, 29 September 2015-28 October 2015 (prof F. Faraci)
I. Mezei
Talks:
1. 5th MATINFO International Conference, 2015 September 2–5, Sapientia Hungarian University of Transylvania, Tg. Mureş, Romania.[link]
Title of talk: Schwarz symmetric solutionf for E-differentiable functionals.
Scientific collaboration:
1. Universita di Catania, Catania, Italy, 19-30 August 2015 (prof F. Faraci).
A. Kristály, A sharp Sobolev interpolation inequality on Finsler manifolds, Journal of Geometric Analysis, Volume 25 (2015) Issue 4, 2226-2240, AIS: 1.864; impact factor: 1.109 [pdf]. C2.II.2
A. Kristály, Sharp Morrey-Sobolev inequalities on complete Riemannian Manifolds, Potential Analysis, Volume 42 (2015), Issue 1, 141-154, AIS: 1.465; impact factor: 0.956 [pdf]. C2.II.2, C2.I.1
K. Perera, P. Pucci, Cs. Varga, An existence result for a class of quasilinear elliptic eigenvalue problems in unbounded domains, Nonlinear Differential Equations and Applications NoDEA, Volume 21 (2014), Issue 3, 441-451, AIS: 1.313; impact factor: 0.796 [pdf]. C2.II.1
B. Breckner, Cs. Varga, A note on gradient-type systems on fractals, Nonlinear Analysis: Real World Applications, Volume 21 (2015), 142-152, AIS: 1.311; impact factor: 2.237 [pdf]. C2.II.1
A. Kristály, I. Rudas, Elliptic problems on the ball endowed with Funk-type metrics, Nonlinear Analysis: Theory Methods and Applications, Volume 119 (2015), 199-208, AIS: 1.148; impact factor: 1.125 [pdf]. C2.II.2
F. Faraci, Cs. Farkas, A quasilinear elliptic problem involving critical Sobolev exponents, Collectanea Mathematica, Volume 66 (2015) Issue 2, 243-259, AIS: 0.837; impact factor: 0.593 [pdf]. C2.II.2
Cs. Farkas, Cs. Varga, Multiple symmetric invariant non trivial solutions for a class of quasilinear elliptic variational systems, Applied Mathematics and Computation, Volume 241 (2014), 347-355, AIS: 0.733; impact factor: 1.345 [pdf]. C2.II.1
I. Mezei, A. É. Molnár, O. Vas, Multiple symmetric solutions for some hemi-variational inequalities, Stud. Univ. Babeș-Bolyai, Volume 9 (2014) Issue 3, 369-384 [pdf]. C2.II.1
A. Kristály
Talks:
1. ICMC - Summer Meeting on Differential Equations (2014 Chapter), Sao Paulo, Brasil, 3-7 February 2014. [link]
Title of talk: Caffarelli-Kohn-Nirenberg inequalities on metric measure spaces: symmetrization and rigidity.
2. ALEL2014-International Conference on Optimization, Seville, Spain, 5-7 June 2014. [link]
Invited speaker. Title of talk: Nash-type equilibria on Riemannian manifolds: the effect of curvature.
3. The 10th AIMS Conference on Dynamical Systems, Differential Equations and Applications, 7-11 July 2014, Madrid, Spain. [link]
Invited speaker. Title of talk: A variational approach to Nash equilibria on Riemannian manifolds.
Scientific collaborations:
1. University of Russe, Bulgaria, 24-31 January, 2014. (prof. S. Tersian)
2. Universita di Catania, Catania, Italy, 14-25 August 2014. (prof. F. Faraci)
3. City University of Hong Kong, Hong Kong, China, 21 September - 20 October 2014. (prof. Ph. G. Ciarlet)
Cs. Varga
Talk:
1. Eötvös Loránd University, Budapest, Hungary, 22 September 2014. [link]
Title of talk: Nonexistence and existence results for Finsler--Laplace equations with--singular weight.
Scientific collaboration:
1. Eötvös Lóránd University, Budapest, Hungary, 2-11 November 2014. (prof. L. Simon)
Cs. Farkas
Talk:
1. The 10th AIMS Conference on Dynamical Systems, Differential Equations and Applications, 7-11 July 2014, Madrid, Spain. [link]
Title of talk: A quasilinear elliptic problem involving critical Sobolev exponents.
Scientific collaborations:
1. University of Russe, Bulgaria, 24-31 January, 2014. (prof. S. Tersian)
2. Universita di Catania, Catania, Italy, 14-25 August 2014. (prof. F. Faraci)
A. Kristály, Nash-type equilibria on Riemannian manifolds:A variational approach, Journal de Mathématiques Pures et Appliquées, Volume 101 (2014), Issue 5, 660-688, AIS: 3.117; impact factor: 1.818 [pdf]. C2.II.2
A. Kristály, S. Ohta, Caffarelli-Kohn-Nirenberg inequality on metric measure spaces with applications, Mathematische Annalen, Volume 357 (2013), Issue 2, 711-726, AIS: 3.220; impact factor: 1.366 [pdf]. C2.I.1, C2.I.3
B. Breckner, Cs. Varga, Multiple solutions of Dirichlet problems on the Sierpinski gasket, Journal of Optimization Theory and Applications, Volume 167 (2015), Issue 3, 842–861, AIS: 1.164; impact factor: 1.159 [pdf]. C2.II.1
H. Lisei, Cs. Varga, A multiplicity result for a class of elliptic problems on compact Riemannian manifolds, Journal of Optimization Theory and Applications, Volume 167 (2015), Issue 3, 912–927, AIS: 1.164; impact factor: 1.159 [pdf]. C2.II.2
A. Kristály
Talk:
1. University of Paris-Sud, Paris, France, 27 May 2013. [link]
Title of talk: Caffarelli-Kohn-Nirenberg inequality on metric measure spaces: symmetrization and rigidity.
Scientific collaborations:
1.University of Rousse, Rousse, Bulgaria, 23-30 August 2013. (prof. T. Gyulov and S. Tersian)
2. Universitat Bern, Bern, Switzerland, 22-31 October 2013. (prof Z. Balogh)
Cs. Varga
Talk:
1. Óbuda University, Budapest, Hungary, 19-21 November 2013.
Title of talk: Multiple solutions of Dirichlet problems and systems of gradient type on the Sierpinski gasket.
Cs. Farkas
Talk:
1. Óbuda University, Budapest, Hungary, 19-21 November 2013.
Title of talk: New conditions for the existence of infinitely many solutions for a quasilinear problem.
Scientific collaborations:
1. University of Rousse, Rousse, Bulgaria, 23-30 August 2013. (prof. T. Gyulov and S. Tersian)
2. Workshop "Geometric Analysis on Riemannian and singular metric spaces", 30 September-4 October, 2013, Como, Italy, participant.
Z. M. Balogh, A. Kristály, Lions-type compactness and Rubik-actions on the Heisenberg group, Calculus of Variations and PDE, Volume 48 (2013), Issue 1-2 , 89-109, AIS: 2.929; impact factor: 1.555 [pdf]. C2.II.3
G. Autuori, P. Pucci, Cs. Varga, Existence theorems for quasilinear elliptic eigenvalue problems in unbounded domains, Advances Differential Equations, Volume 18 (2013), Numbers 1-2 , 1-48, AIS: 1.543; impact factor: 0.917 [pdf]. C2.II.1
Cs. Farkas, I. Mezei, Group-invariant multiple solutions for quasilinear elliptic problems on strip-like domains, Nonlinear Analysis TMA, Volume 79 (2013), 238-246, AIS: 1.148; impact factor: 1.125 [pdf]. C2.II.1
F. Faraci, A. Iannizzotto, Cs. Varga, Multiplicity results for constrained Neumann problems, Contemporary Math. AMS volume dedicated to Professor Patrizia Pucci on the occasion of her 60th birthday, 2013 [pdf]. C2.II.2
A. Kristály
Talks:
1. Budapest University of Technology and Economics, Budapest, Hungary, 29 January-5 February 2012. Lectures Series, speaker. [link]
2. The 10th International Conference on "Fixed point theory and its applications", Babeș-Bolyai University, Cluj-Napoca, Romania, 9-15 July 2012. [link]
Title of talk: Nash-type equilibria on Riemannian manifolds: a variational approach.
3. Nonlinear Difference and Differential Equations and their Applications, Russe, Bulgaria, 4-6 October 2012.
Title of talk: Anisotropic problems in the presence of asymmetric Minkowski norms.
4. University of Kyoto, Kyoto, Japan, Octomber 2012.
Title of talk: Caffarelli-Kohn-Nirenberg inequalities on Finsler manifolds.
5. University of Bern, Bern, Switzerland, November 2012. [link]
Title of talk: Best constants in some Hardy-Sobolev inequalities.
Scientific collaborations:
1. University of Ljubljana, Ljubljana, Slovenia, 12-24 August 2012. (prof. D. Repovs)
2. University of Kyoto, Kyoto, Japan, 5-12 Octomber 2012. (prof. S. Ohta.)
3. University of Bern, Bern, Switzerland, 1-30 November 2012. (prof Z. Balogh)
Cs. Varga
Talks:
1. Workshop on Nonlinear Partial Differential Equations on the occasion of the sixtieth birthday of Patrizia Pucci, Perugia, 28 May- 1 June 2012. [link]
Title of talk: Systems of nonlinear hemivariational inequalities and applications.
2. Nonlinear Difference and Differential Equations and their Applications, Russe, Bulgaria, 4-6 October 2012.
Title of talk: Existence theorems for quasilinear elliptic problems in unbounded domains.
3. Eötvös Loránd University, Budapest, Hungary, November 2012. [link]
Title of talk: Existence theorems for quasilinear elliptic eigenvalue problems in unbounded domains.
Scientific collaboration:
1. Eötvös Loránd University, Budapest, Hungary, 3-11 November 2012.(prof. L. Simon.)
Cs. Farkas
Talks:
1. Workshop on Nonlinear Partial Differential Equations on the occasion of the sixtieth birthday of Patrizia Pucci, Perugia, 28 May- 1 June 2012. [link]
Title of poster: Multiplicity results for a Neumann--problem on strip-like domains.
2. The 10th International Conference on "Fixed point theory and its applications", Babeș-Bolyai University, Cluj-Napoca, Romania, 9-15 July 2012. [link]
Title of poster: Multiplicity results in strip-like domains.
3. Nonlinear Difference and Differential Equations and their Applications, Russe, Bulgaria, 4-6 October 2012.
Title of talk: Some multiplicity results on strip like domains.
Scientific collaborations:
1. Budapest University of Technology and Economics, Budapest, Hungary, 29 Januar-5 February 2012. Mini Workshop, participant. [link]
2. Central European University, Budapest, Hungary, 23-31 July 2012 and 11-13 October 2012. (prof. Gh. Morosanu)
I. Mezei
Scientific collaboration:
1. Budapest University of Technology and Economics, Budapest, Hungary, 29 January-5 February 2012. Lectures Series, participant. [link]
2. Central European University, Budapest, Hungary, 20 August-1 September 2012 (prof. Gh. Morosanu)
A. Kristály, Geometric aspects of Moser-Trudinger inequalities on complete non-compact Riemannian manifolds, submitted, November 2015 [pdf]. C2.II.2
Z. Balogh, A. Kristály, K. Sipos, Geometric inequalities on Heisenberg groups, submitted, June 2016 [pdf]. C2.II.3
E. Barbosa, A. Kristály, Second-order Sobolev inequalities on Riemannian manifolds with nonnegative Ricci curvature, submitted, August 2016 [pdf]. C2.II.2
F. Faraci, Cs. Farkas, A. Kristály, Multipolar Hardy inequalities on Riemannian manifolds. submitted, September 2016 [pdf]. C2.I.2, C2.II.2
Papers in preparation
I. Mezei, Cs. Varga, O. Vas, Existence and non-existence results on Minkowski spaces.
1. In the period of 07 February - 31 December 2013, I. Mezei (young researcher) was on a maternity leave.
2. On 31 October 2014, Cs. Farkas defended his PhD thesis entitled "Symmetrization methods in the study of elliptic problems". [link | summary]
3. Both AIS and IF are taken from the 2016 lists provided by UEFISCDI