My research interests are in Partial Differential Equations (PDEs). In particular, I am interested in regularity theory for classes of elliptic/degenerate equations, such as elliptic/degenerate fully nonlinear operators, p-Laplacian operator, porous medium equation, etc. Currently, I am working on regularity theory for local and nonlocal, and shape optimization problems.
Submitted Papers
C. Alcantara, M. Santos, and J.M. Urbano. Gradient regularity for a class of singular or degenerate elliptic equations and contributions to the $C^{p'}-$conjecture.
C. Alcantara and M. Santos. Regularity theory for the normalized p-Laplacian equation with an arbitrary degeneracy law.
C. Alcantara and M. Santos. Global fractional Sobolev regularity for fully nonlinear elliptic equations.
D. Mazzoleni, M. Santos, and H. Tavares. Free boundary regularity for a spectral optimal partition problem with volume and inclusion constraints
D. Prazeres and M. Santos. Optimal Regularity for Fully Nonlinear Nonlocal Equations with Unbounded Source Terms
J.V da Silva, M. Santos, and M. Soares. Higher regularity estimates for solutions to $\infty$-Laplacian-type models.
Published Papers
P. Andrade, E. Moreira dos Santos, M. Santos and H. Tavares. Spectral partition problems with volume and inclusion constraints. SIAM Journal on Mathematical Analysis (2024)
P. Andrade, J. V. da Silva, G. Rampasso and M. Santos. Sharp regularity estimates for a singular inhomogeneous (m, p)-Laplacian equation. Potential Analysis (2024)
J. V. da Silva and M. Santos. Schauder and Calderón-Zygmund type estimates for fully nonlinear parabolic equations under "small ellipticity aperture" and applications. Nonlinear Analysis (2024)
P. Andrade, D. Prazeres and M. Santos. Regularity estimates for fully nonlinear integro-differential equations with nonhomogeneous degeneracy. Nonlinearity (2024)
E. Pimentel and M. Santos, Fully nonlinear free transmission problems. Interfaces and free boundaries (2023)
H. Chang-Lara and M. Santos, Hölder regularity for non-variational porous media type equations. J. Differential Equations (2023)
P. Andrade and M. Santos, Improved regularity for the parabolic normalized p-Laplace equation. Calc. Var. Partial Differential Equations (2022)
E. Pimentel, M. Santos and E. Teixeira, Fractional Sobolev regularity for fully nonlinear elliptic equations. Comm. Partial Differential Equations (2022)
P. Andrade, G. Rampasso and M. Santos, Geometric regularity theory for a time-dependent Isaacs equation. Nonlinear Differential Equations and Applications NoDEA (2022)
E. Pimentel and M. Santos, Improved regularity for the porous medium equation along zero level-sets. Israel Journal of Mathematics (2021)
E. Pimentel, G. Rampasso and M. Santos, Improved regularity for the p-Poisson equation. Nonlinearity (2020)
R. Leitão, E. Pimentel and M. Santos, Geometric regularity for elliptic equations in double-divergence form. Analysis & PDE (2020)
E. Pimentel and M. Santos, Asymptotic Methods in Regularity Theory for Nonlinear Elliptic Equations: A Survey. Springer INdAM Series. 28ed.: Springer International Publishing (2018)