Welcome to the Personal webpage of Bruno Premoselli 

Publications: 

• Compactness results for Sign-Changing Solutions of critical nonlinear elliptic equations of low energy  (with H. Cheikh-Ali), 41 pages, 2024. arXiv:2412.00817

• Non-existence of minimizers for the second conformal eigenvalue near the round sphere in low dimensions (with J. Vétois), 35 pages, 2024. arXiv:2408.07823

• One-bubble nodal blow-up for asymptotically critical stationary Schrödinger-type equation (with F. Robert), 33 pages, 2024. Accepted for publication in Journal of Functional Analyis arXiv:2404.16384. 

• Classification of radial blow-up at the first critical exponent for the Lin-Ni-Takagi problem in the ball (with D. Bonheure and J.-B. Casteras), 37 pages, 2022. Accepted for publication in Mathematische Annalen. arXiv:2211.08962.

• Sign-changing blow-up for the Yamabe equation at the lowest energy level (with J. Vetois), Advances in Mathematics 410 Part B, 2022. arXiv:2206.08770

• Stability and Instability results for sign-changing solutions to second-order critical elliptic equations (with J. Vetois), Journal de Mathématiques Pures et Appliquées, no. 167 (November 2022), 257-293. arXiv:2201.05679

• A priori estimates for finite-energy sign-changing blowing-up solutions of critical elliptic equations, International Mathematical Research Notices, Vol 2024, Issue 6, March 2024, 5212–5273. arXiv:2111.02470

• Towers of bubbles for Yamabe-type equations and for the Brézis-Nirenberg problem in dimensions $n \ge 7$. Journal of Geometric Analysis no. 32, Article number 73 (2022). arXiv:2009.01515

• Singular perturbations of critical nonlinear elliptic equations in dimension $3$, 21 pages, 2020. Discrete and Continuous Dynamical Systems, no. 41 (2021), issue 11, 5087-5103.  

• Compactness of sign-changing solutions to scalar curvature-type equations with bounded negative part (with J. Vétois),  J. Differential Equations 266 (2019), no. 11, 7416–7458. 

• Examples of compact Einstein four-manifolds with negative curvature (with J. Fine), J. Amer. Math. Soc. 33 (2020), 991-1038. arXiv:1802.00608

• Bubbling above the threshold of the scalar curvature in dimensions four and five (with P-D. Thizy), Calculus of Variations and PDEs no. 57, Article number: 147 (2018), 39 pages.  hal-01805092

• A pointwise finite-dimensional reduction method for Einstein-Lichnerowicz type systems: the six-dimensional case, Nonlinear Analysis no. 172 (2018), 200--215.

• A pointwise finite-dimensional reduction method for a fully coupled system of Einstein-Lichnerowicz type, Communications in Contemporary Mathematics 20 (2018), no. 6, 1750076, 72 pp. arXiv:1605.05468

• Non-compactness and infinite number of conformal initial data sets in high dimensions (with J. Wei), Journal of Functional Analysis 270 (2016), no.2, 718--747. arXiv:1505.02806 

• Stability and instability of the $n$-dimensional Einstein-Lichnerowicz constraints system,  International Mathematical Research Notices Vol. 2016 no.8, 1951-2025. arXiv:1502.04233

• Stability of the Einstein-Lichnerowicz constraints system (with O. Druet), Mathematische Annalen 362 (2015), no.3, 839-886. arXiv:1312.6574

• Effective multiplicity for the Einstein-scalar field Lichnerowicz equation, Calculus of variations and Partial Differential Equations 53 (2015), no.1, 29-64. arXiv:1307.2416

• The Einstein-scalar field constraint system in the positive case, Communications in Mathematical Physics 326 (2014), no. 2, 543-557. arXiv:1301.5792
  
  

Conference Proceedings:

• Negatively curved Einstein metrics on ramified covers of closed four-dimensional hyperbolic manifolds. To appear in Actes du Séminaire de Théorie Spectrale et Géométrie de l'Insitut Fourier

• A pointwise finite-dimensional reduction method for Einstein-Lichnerowciz type systems, Proceedings of the BruTo PDE's Conference (Torino, 2--5 May 2016). Rend. Semin. Mat. Univ. Politec. Torino 74 (2016), no. 2, 81–93.