Research

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 and shape optimization problems.

• Curriculum Vitae

• Researchgate

• Google scholar

• Mathscinet

• ORCID

Submitted Papers

• P. Andrade, E. Moreira dos Santos, H. Tavares. Spectral partition problems with volume and inclusion constraints

• P. Andrade, J. V. da Silva, G. Rampasso and M. Santos. Sharp regularity estimates for a singular inhomogeneous (m, p)-Laplacian equation

Published Papers

• J. V. da Silva and M. Santos. Schauder and Calderón-Zygmund type estimates for fully nonlinear parabolic equations under "small ellipticity aperture" and applications. To appear in 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)