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):

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