|Address|| Department of Mathematics,
17 University Ave. Ste 1701
San Juan PR, 00925-2537
|Office||NCN II C-112|
|Telephone||(787) 764-0000 88258|
EducationPhD, University of Ulm (Germany), 2002
Research InterestsTeoria de potencial; Ecuaciones diferenciales parciales lineales y no lineales; Análisis funcional; Ecuaciones de evolución; semigrupos de operadores.
- (with H. Antil) Optimal control of the coefficient for fractional and regional fractional p-Laplace equations: Approximation and convergence. Mathematical Control and Related Fields, to appear.
- (with U. Biccari and E. Zuazua) Local regularity for fractional heat equations. SEMA- SIMAI Springer Series, to appear.
- Mahamadi Warma. On a fractional (s, p)-Dirichlet-to-Neumann operator on bounded Lipschitz domains. Journal of Elliptic and Parabolic Equation 4 (2018), 223--269.
- Mahamadi Warma (with W.Arendt and A.F.M. Ter Elst) Fractional powers of sectorial operators via the Dirichlet-to-Neumann operator. Comm. Partial Differential Equations 43 (2018), no. 1, 1–24.
- (with V. Keyantuo and C. Lizama) Existence, regularity and representation of solutions of fractional wave equations. Electronic Journal of Differential Equations 2017 (2017), No. 222, pp. 1-42.
- On the approximate controllability from the boundary for fractional wave equations. Applicable Analysis 96 (2017), 2291–2315.
- (with H. Antil and J. Pfefferer) A note on semilinear fractional diffusion equation: analysis and discretization. Mathematical Modelling and Numerical Analysis. ESAIM: M2AN 51 (2017), 2049–2067.
- (with C. G. Gal). Nonlinear elliptic boundary value problems at resonance with nonlinear Wentzell-Robin type boundary conditions. Advances in Mathematical Physics 2017 (2017), Article ID 5196513, 20 pages.
- (with U. Biccari and E. Zuazua) Addendum: Local elliptic regularity for the Dirichlet fractional Laplacian. Adv. Nonlinear Stud. 17 (2017), 837–839.
- (with U. Biccari and E. Zuazua) Local elliptic regularity for the Dirichlet fractional Laplacian. Advanced Nonlinear Studies 17 (2017), 387–409.
- (with C. G. Gal) Nonlocal transmission problems with fractional diffusion and bound- ary conditions on non-smooth interfaces. Communication in Partial Differential Equations 42 (2017), 579–625.
- (with C. G. Gal) On some degenerate non-local parabolic equations associated with the fractional p-Laplacian. Dynamics of PDE 14 (2017), 47–77.
- (with C.G. Gal). Long-term behavior of reaction-diffusion equations with nonlocal boundary conditions on nonsmooth domains. Zeitschrift fu ̈r angewandte Mathematik und Physik ZAMP 67 (2016), no. 4, Art. 83, 42 pp.
- (with C. G. Gal) Bounded solutions for nonlocal boundary valued problems on Lipschitz manifolds with boundary. Advanced Nonlinear Studies 16 (2016), 529–550.
- (with V. Keyantuo and C. Lizama). Existence, regularity and representation of solu- tions of time fractional diffusion equations. Advances in Differential Equations 21 (9/10) (2016), 837–886.
- (with C. G. Gal) Elliptic and parabolic equations with fractional diffusion and dynamic boundary conditions. Evolution Equations and Control Theory 5 (2016), 61– 103.
- (with V. Keyantuo) On the interior approximate controllability for fractional wave equa tions. Discrete Contin. Dyn. Syst. Ser. A 36 (2016), 3719–3739.
- Local Lipschitz continuity of the inverse of the fractional p-Laplacian, Ho ̈lder type continuity and continuous dependence of solutions to associated parabolic equations on bounded domains. Nonlinear Analysis 135 (2016), 129–157.
- The fractional Neumann and Robin boundary condition for the fractional p-Laplacian on open sets. NoDEA Nonlinear Differential Equations Appl. 23 (2016), 1–46.
- (with C. G. Gal) Transmission problems with nonlocal Wentzell type boundary conditions and rough dynamic interfaces. Nonlinearity 29 (2016), 161–197.
- (wth C. G. Gal) Reaction-diffusion equations with fractional diffusion on non-smooth domains with various boundary conditions. Discrete Contin. Dyn. Syst. Ser. A 36 (2016) 1279–1319.
- A fractional Dirichlet-to-Neumann operator. Commun. Pure Appl. Anal. 14 (2015), 2043–2067.
- The fractional relative capacity and the fractional Laplacian with Neumann and Robin boundary conditions on open sets. Potential Analysis 42 (2015) , 499–547.
- The p-Laplace operator with the nonlocal Robin boundary conditions on arbitrary open sets. Ann. Mat. Pura Appl. 193 (2014), 203–235.
- (with P. Sacks) Semi-linear elliptic and elliptic-parabolic equations with Wentzell boundary conditions and L1-data. Discrete Contin. Dyn. Syst. Ser. A 34 (2014), 763–789.
- (with V. Keyantuo and C. Lizama). Spectral criteria for solvability of boundary value problems and positivity of solutions of time-fractional differential equations. Abstract Applied Analysis (2013), Article ID 614328, 11 pages.
- (with V. Keyantuo and C. Lizama) Asymptotic behavior of fractional order semilinear evolution equations. Differential Integral Equations 26 (2013), 757–780.
- Semi linear parabolic equations with nonlinear general Wentzell boundary conditions. Discrete Contin. Dyn. Syst. Ser. A 33 (2013), 5493–5506.
- (with Ciprian G. Gal) Existence of bounded solutions for a class of quasilinear elliptic systems on manifolds with boundary. J. Differential Equations 255 (2013), 151– 192.
- (with R. Chill) A Riesz type representation for lower semicontinuous, monotone, local functionals on Cc(X)+. Nonlinear Analysis 85 (2013), 17–22.
- Parabolic and elliptic problems with general Wentzell boundary conditions on Lipschitz domains. Commun. Pure Appl. Anal. 12 (2013), 1881–1905.
- (with R. Chill) Dirichlet and Neumann boundary conditions for the p-Laplace operator: What is in between? Proceedings of the Royal Society of Edinburgh, Section A 142 (2012), 975–1002.
- Regularity and well-posedness of some quasi-linear elliptic and parabolic problems with nonlinear general Wentzell boundary conditions on nonsmooth domains. Nonlinear Analysis 75 (2012) 5561–5588.
- (with E. Alvarez-Pardo). The one-dimensional wave equation with nonlocal Robin boundary conditions. Archiv der Mathematik (Basel) 96 (2011), 177–186.
- Analyticity on L1 of the heat semigroup with Wentzell boundary conditions. Archiv der Mathematik (Basel) 94 (2010), 85-89.
- (with M. Biegert). Existence of solutions to some quasi-linear PDEs with generalized Robin boundary conditions. Nonlinear Analysis 73 (2010), 1853-1863.
- (with M. Biegert). Some quasi-linear elliptic equations with inhomogeneous generalized Robin boundary conditions on “bad” domains. Advances in Differential Equations 15 (2010), 893-924.
- (with A. Velez-Santiago). A class of quasi-linear parabolic and elliptic equations with nonlocal Robin boundary conditions. J. Mathematical Analysis and Applications 372 (2010), 120-139.
- (with C. G. Gal). Well-posedness and the global attractor of some quasi-linear parabolic equations with nonlinear dynamic boundary conditions. Differential and Integral Equations 23 (2010), 327–358.
- (with M. Biegert). The heat equation with nonlinear generalized Robin boundary conditions. J. Differential Equations 247 (2009), 1949–1979.
- An ultracontractivity property for semigroups generated by the p-Lapalcian with non- linear Wentzell-Robin boundary conditions. Advances in Differential Equations 14 (2009), 771–800.
- (with R. Chill and V. Keyantuo). Generation of cosine families on Lp(0,1) by elliptic operators with Robin boundary conditions. Birkhau ̈ser. Functional Analysis and Evolution Equations. 2008, 113–130.
- Quasilinear parabolic equations with nonlinear Wentzell-Robin type boundary conditions. J. Math. Anal. Appl. 336 (2007), 1132-1148.
- with V. Keyantuo) The wave equation with Wentzell-Robin boundary conditions on Lp -spaces. J. Differential Equations, 229 (2006), 680-697.
- (with M. Biegert) Regularity in capacity and the Dirichlet Laplacian. Potential Anal. 25 (2006), 289-305.
- (with W. Arendt) Dirichlet and Neumann boundary conditions: What is in between? J. Evol. Equ. 3 (2003), 119-135.
- Wentzell-Robin boundary conditions on C [0, 1]. Semigroup Forum 66 (2003), 162-170.
Grants and Awards
- AFOSR Grant FA9550-18-1-0242. (PI) Nonlocal PDEs: Analysis, Control and Beyond. June 2018–May 2021 (Total: $456,494).
- AFOSR Grant FA9550-15-1-0027. (PI) Dynamics, Control and Numerics for Fractional Partial Differential Equations. December 2014--May 2018 (Total: $450,438)
- ARO Grant W911NF-17-1-0286. (PI) Workshop on Dynamics, Control and Numerics for Fractional PDEs. May 2017-- December 31, 2018. (Total: $18,600.00)
- AFOSR Grant FA9550-17-1-0524. (PI) Workshop on Dynamics, Control and Numerics for Fractional PDEs. September 30, 2017 -- March 31, 2019. (Total: $39, 853.00)