Mouhamed Moustapha Fall
Publications
Research interest:
(A) Primary interest: Partial Differential Equations and Differential Geometry.
Focus: Constant Mean Curvature hyper-surfaces; Isoperimetric inequalities involving perimeter and eigenvalues on Riemannian manifolds; Hardy and Hardy-Sobolev inequalities; qualitative properties of Partial Differential Equations; overdetermined problems, etc.
(B) Other interests: Mathematical modeling, Agent Based Modeling, Predator-Preys, etc.
Publications (A):
61) M.M. Fall, T. Weth, Second radial eigenfunctions to a fractional Dirichlet problem and uniqueness for a semilinear equation Preprint 2024 (submitted). File.pdf
60) M.M. Fall and T. Weth, Nonradial nondegeneracy and uniqueness of positive solutions to a class of fractional semilinear equations Preprint 2024 (submitted). File.pdf.
59) M. M. Fall, M. Ghimenti, A. M. Micheletti, A. Pistoia, Generic properties of eigenvalues of the fractional Laplacian Calc. Var. Partial Differential Equations 62 (2023), no. 8, Paper No. 233, 17 pp. https://doi.org/10.1007/s00526-023-02574-8 File.pdf
58) M. M. Fall, I. A. Minlend T. Weth: The Schiffer problem on the cylinder and on the $2$-sphere: Preprint 2023 (To appear in JEMS) File.pdf.
57) A. Attiogbe, M. M. Fall, T. Weth: Short time existence and smoothness of the nonlocal mean curvature flow of graphs: Mathematische Annalen. https://doi.org/10.1007/s00208-023-02737-0 File.pdf
56) M. M. Fall, I. A. Minlend, T. Weth: On an electrostatic problem and a new class of exceptional domains in R^3: SIAM J. Math. Anal. 55 (2023), no. 3, 2347–2376. https://doi.org/10.1137/22M148754 File.pdf
55) S. M. Djitte, M. M. Fall, T. Weth: A generalized fractional Pohozaev identity and applications: Advanced in Calculus of Variations DOI: 10.1515/acv-2022-0003 File.pdf
54) N. Abatangelo, M. M. Fall, R. Y. Temgoua: A Hopf lemma for the regional fractional Laplacian: Ann. Mat. Pura Appl. (4) 202 (2023), no. 1, 95–113. https://doi.org/10.1007/s10231-022-01234-6 File.pdf
53) M. M. Fall, R. Y. Temgoua: Existence results for nonlocal problems governed by regional fractional Laplacian: NoDEA Nonlinear Differential Equations Appl. 30 (2023), no. 2, Paper No. 18, 32 pp. https://doi.org/10.1007/s00030-022-00826-8 File.pdf
52) M. M. Fall, T. Mengesha, A. Schikorra, S. Yeepo: Calderon-Zygmund theory for non-convolution type nonlocal equations with continuous coefficient. Partial Differential Equations and Applications (2022) 3:24. https://doi.org/10.1007/s42985-022-00161-8 File.pdf
51) M. M. Fall, X. Ros-Oton: Global Schauder theory for minimizers of the H^s(\Omega) energy. J. Funct. Anal. 283 (2022), no. 3, Paper No. 109523. https://doi.org/10.1016/j.jfa.2022.109523 File.pdf
50) A. Attiogbe, El. H. A. Thiam, M. M. Fall: Nonlocal diffusion of smooth sets. Mathematics in Engineering 2022, Volume 4, Issue 2: 1-22. doi: 10.3934/mine.2022009 File.pdf
49) M. M. Fall, I. A. Minlend and J. Ratzkin: Foliation of an asymptotically flat end by critical capacitors. Journal of Geometric Analysis, 32, no. 54 (2022). https://doi.org/10.1007/s12220-021-00746-6 File.pdf
48) M. M. Fall, Regional fractional Laplacians: Boundary regularity. Journal of Differential Equations 320 (2022) 598–658. https://doi.org/10.1016/j.jde.2022.02.040 File.pdf
47) M. M. Fall, P. A. Feulefack, R.Y. Temgoua, T. Weth, Morse index versus radial symmetry for fractional Dirichlet problems. Advances in Mathematics 384(5):107728 (2021). https://doi.org/10.1016/j.aim.2021.107728 File.pdf
46) S. M. Djitte, M. M. Fall, T. Weth, A fractional Hadamard formula and applications. Calc. Var. Partial Differential Equations, 60 (2021), no. 231. https://doi.org/10.1007/s00526-021-02094-3 File.pdf
45) Fall M. M., and Jarohs S., Gradient estimates in fractional Dirichlet problems. Potential Anal. 54 (2021), no. 4, 627–636. 35 (47). https://doi.org/10.1007/s11118-020-09842-8 File.pdf
44) Fall M. M., Regularity results for nonlocal equations and applications. Calc. Var. Partial Differential Equations 59 (2020), no. 5, 181. https://doi.org/10.1007/s00526-020-01821-6 File.pdf
43) Abatangelo N., Dipierro S., Fall M. M., Jarohs S., Saldaña A. Positive powers of the Laplacian in the half-space under Dirichlet boundary conditions. Discrete & Continuous Dynamical Systems - A, 2019, 39 (3) : 1205-1235. doi: 10.3934/dcds.2019052. File.pdf
42) Fall M.M., Constant Nonlocal Mean Curvature Surfaces and related problems. Proc. Int. Cong. of Math. – 2018 Rio de Janeiro, Vol. 1 (21–30) DOI: 10.9999/icm2018-v1-p21. File.pdf
41) Fall M.M. and Weth T., Critical domains for the first nonzero Neumann eigenvalue in Riemannian manifolds. J. Geom. Anal. 29 (2019), no. 4, 3221–3247. https://doi.org/10.1007/s12220-018-00115-w File.pdf
40) Fall M.M., Periodic patterns for a model involving short-range and long-range interactions. Nonlinear Analysis 175 (2018) 73–107. https://doi.org/10.1016/j.na.2018.05.009 File.pdf
39) Fall M.M., Regularity estimates for nonlocal Schrödinger equations. Discrete & Continuous Dynamical Systems - A, 2019, 39 (3) : 1405-1456. doi: 10.3934/dcds.2019061. File.pdf
38) Fall M.M., Felli V., Ferrero A. and Niang A., Asymptotic expansions and unique continuation at Dirichlet-Neumann boundary junctions for planar elliptic equations Mathematics in Engineering, 2018, 1(1): 84-117. doi: 10.3934/Mine.2018.1.84. File.pdf
37) Chen H., Fall M.M. and Zhang B., On isolated singularities of Kirchhoff--type Laplacian problems. Adv. Nonlinear Anal. 10 (2021), no. 1, 102–120. https://doi.org/10.1515/anona-2020-0103 File.pdf .
36) Fall M.M. and Thiam E.A., Hardy-Sobolev inequality with singularity a curve. Topol. Methods Nonlinear Anal. 51 (2018), 151–181. DOI: 10.12775/TMNA.2017.045 File.pdf
35) Cabré X., Fall M.M. and Weth T., Near-sphere lattices with constant nonlocal mean curvature. Math. Ann. (2018) 370(3), 1513-1569. File.pdf
34) Fall M.M., Minlend I.A. and Weth T., Serrin's overdetermined problem on the sphere. Calc. Var. Partial Differential Equations 57 (2018), no. 1,57:3. https://doi.org/10.1007/s00208-017-1559-6 File.pdf
33) Fall M.M., Minlend I.A. and Weth T., Unbounded periodic solutions to Serrin's overdetermined boundary value problem. Arch. Ration. Mech. Anal. 223 (2017), no. 2, 737–759. https://doi.org/10.1007/s00205-016-1044-5 File.pdf
32) X. Cabré, M.M. Fall and T. Weth, Delauney Hypersurfaces with constant nonlocal mean curvature. J. Math. Pures Appl. 110 (2018) 32–70. https://doi.org/10.1016/j.matpur.2017.07.005 File.pdf
31) T. Caroll, M.M. Fall and J. Ratzkin, On the rate of change of the best constant in the Sobolev inequality. Math. Nachr. 290 (2017), no. 14-15, 2185–2197. DOI: 10.1002/mana.201600277 File.pdf
30) Fall, Mouhamed Moustapha; Weth, Tobias, Liouville theorems for a general class of nonlocal operators. Potential Anal. 45 (2016), no. 1, 187–200. https://doi.org/10.1007/s11118-016-9546-1 File.pdf
29) Cabré X., Fall M.M. Solà-Morales J. and Weth T., Curves and surfaces with constant nonlocal mean curvature: meeting Alexandrov and Delaunay. J. Reine Angew. Math. 745 (2018), 253–280. https://doi.org/10.1515/crelle-2015-0117 File.pdf
28) M.M. Fall and T. Weth, Profile expansion for the first nontrivial Steklov eigenvalue in Riemannian manifolds. Comm. Anal. Geom. 25 (2017), no. 2, 431–463. DOI: 10.4310/CAG.2017.v25.n2.a6 File.pdf
27) Evéquoz G. and Fall M.M., Positive solutions to some nonlinear fractional Schrödinger equation via a Min-Max procedure. (Submitted) File.pdf
26) Cho Y., Fall M.M., Hajaiej H., Markowich P.A., Trabelsi S., Orbital stability of standing waves of a class of fractional Schrodinger equations with a general Hartree-type integrand. Anal. Appl. (Singap.) 15 (2017), no. 5, 699–729. DOI: 10.1142/S0219530516500056 File.pdf
25) Fall M.M., Semilinear elliptic equations for the fractional Laplacian with Hardy potential. Nonlinear Anal. 193 (2020), 111311. https://doi.org/10.1016/j.na.2018.07.008 File.pdf
24) Fall M.M., Entire s-harmonic functions are affine. Proc. Amer. Math. Soc. 144 (2016), no. 6, 2587-2592. DOI: 10.1090/proc/13021 File.pdf
23) Fall M.M., Mahmoudi F. and Valdinoci E., Ground states and concentration phenomena for the fractional Schrödinger equation. Nonlinearity 28 (2015), no. 6, 1937–1961. DOI 10.1088/0951-7715/28/6/1937 File.pdf
22) Fall M.M.,Minlend I.A., and Thiam E. H. A. , The role of the mean curvature in a Hardy-Sobolev trace inequality. Nonlinear Differ. Equ. Appl, V. 22, 5 (2015), 1047-1066. DOI: 10.1007/s00030-015-0313-6. File.pdf
21) Fall M.M. and Weth T., Monotonicity and nonexistence results for some fractional elliptic problems in the half space. Commun. Contemp. Math. 18 (2016), no. 1, 1550012, 25 pp. File.pdf
20) Fall M.M. and Felli V., Unique continuation properties for the relativistic Schrördinger operator with singular potential. Discrete Contin. Dyn. Syst. 35 (2015), no. 12, 5827-5867.File.pdf
19) Fall M.M. and Jarohs S., Overdetermined problems with fractional laplacian. ESAIM Control Optim. Calc. Var. 21 (2015), no. 4, 924-938. File.pdf
18) Fall M.M. and Minlend I.A., Serrin's over-determined problems on Riemannian manifolds. Adv. Calc. Var. 8 (2015), no. 4, 371-400. File.pdf
17) Fall, Mouhamed Moustapha and Felli, Veronica, Sharp essentially self-adjointness for the relativistic Schr\"ordinger operator with singular potential. J. Funct. Anal. 267 (2014), no. 6, 1851-1877. File.pdf
16) Fall, Mouhamed Moustapha; Weth, Tobias Sharp local upper bound of the first non-zero Neumann eigenvalue in Riemannian manifolds. Calc. Var. Partial Differential Equations 51 (2014), no. 1-2, 217-242. File.pdf
15) Fall, Mouhamed Moustapha; Valdinoci, Enrico; Uniqueness and Nondegeneracy of Positive Solutions of (−Δ)^s u+u=u^p in R^N when s is Close to 1. Comm. Math. Phys. 329 (2014), no. 1, 383-404. File.pdf
14) Fall, Mouhamed Moustapha; Mahmoudi, Fethi, Weighted Hardy inequality with higher dimensional singularity on the boundary. Calc. Var. Partial Differential Equations. 50 (2014), no. 3-4, 779–798. File.pdf
13) Fall, Mouhamed Moustapha; Felli, Veronica Unique continuation property and local asymptotics of solutions to fractional elliptic equations. Comm. Partial Differential Equations. 39: 1-44, 2014. File.pdf
12) Fall, Mouhamed Moustapha Nonexistence of distributional supersolutions of a semilinear elliptic equation with Hardy potential. J. Funct. Anal., Vol 264, no 3(2013) 661-690. File.pdf
11) Fall, Mouhamed Moustapha; Weth, Tobias Nonexistence results for a class of fractional elliptic boundary value problems. J. Funct. Anal., Vol. 263, no. 8 (2012) 2205--2227. File.pdf
10) Fall, Mouhamed Moustapha Embedded disc-type surfaces with large constant mean curvature and free boundaries. Commun. Contemp. Math., Vol. 14, No. 6 (2012) 1250037.
9) Fall, Mouhamed Moustapha; Musina, Roberta Hardy-Poincaré inequalities with boundary singularities. Proc. Roy. Soc. Edinburgh. A 142 (2012) 1--18. File.pdf
8) Fall, Mouhamed Moustapha On the Hardy Poincaré inequality with boundary singularities. Commun. Contemp. Math., Vol. 14, No. 3 (2012) 1250019. File.pdf
7) Fall, Mouhamed Moustapha A note on Hardy's inequalities with boundary singularities. Nonlinear Anal. 75 (2012) no. 2, 951--963. File.pdf
6) Fall, Mouhamed Moustapha; Musina, Roberta Sharp nonexistence results for a linear elliptic inequality involving Hardy and Leray potentials. Journal of Inequalities and Applications Volume 2011, Article ID 917201, 21 pages doi:10.1155/2011/917201. File.pdf
5) Fall, Mouhamed Moustapha Area-minimizing regions with small volume in Riemannian manifolds with boundary. Pacific J. Math. 244 (2010), no. 2, 235--260.
4) Fall, Mouhamed Moustapha Some local eigenvalue estimates involving curvatures. Calc. Var. Partial Differential Equations 36 (2009), no. 3, 437--451. https://link.springer.com/article/10.1007/s00526-009-0236-3
3) Fall, Mouhamed Moustapha; Mercuri, Carlo Minimal disc-type surfaces embedded in a perturbed cylinder. Differential Integral Equations 22 (2009), no. 11-12, 1115--1124.
2) Fall, Mouhamed Moustapha; Mercuri, Carlo Foliations of small tubes in Riemannian manifolds by capillary minimal discs. Nonlinear Anal. 70 (2009), no. 12, 4422--4440. DOI: 10.57262/die/1356019407
1) Fall, Mouhamed Moustapha; Mahmoudi, Fethi Hypersurfaces with free boundary and large constant mean curvature: concentration along submanifolds. Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 7 (2008), no. 3, 407--446. File.pdf
Publications (B):
1) K. Owusu, E. Acevedo-Trejos, M. M. Fall, A. Merico, Effects of cooperation and different characteristics of Marine Protected Areas in a simulated small-scale fishery. November 2020. Ecological Complexity 44:100876. DOI: 10.1016/j.ecocom.2020.100876
2) M. M. Fall, B. M. Ndiaye, D. Seck, O. Seydi, Analysis of COVID-19 evolution in Senegal: impact of health care capacity (Submitted). PDF.file
3) K. A. Owusu, M. M. Fall, An agent-based model to assess the impact of non-pharmaceutical interventions on the spread of COVID-19 for Dakar region, Senegal. Link: https://github.com/kwabenaOwusu/CoronaInterventionsABM