Postdoctoral position at Department of Mathematics, Analysis and Partial Differential Equations
My primary interest in mathematics concerns the regularity theory for partial differential equations, specially the study of the regularity of solutions and their level sets. The topic lies in the interface of analysis and geometry. I have a great enthusiasm in exploring new topics and developing novel techniques that combine these areas. Particularly, I am interested in free boundary problems and homogenization problems.
Keywords: analysis partial differential equations regularity free boundary problems homogenization problems
Recent research interests
Recently, I gained interests, among other issues in the PDE theory, to vectorial maps with free boundaries. Prototypes are harmonic maps into manifolds-with-boundary. These mappings were studied a few decades ago from the perspective of the theory of harmonic maps. However, little was known (as opposed to harmonic maps from manifolds-with-boundary) about the behavior of the mappings near their free boundaries, which are given by the pre-image of the boundary of the target manifold. Recent collaborations and ongoing projections of mine is giving a new perspective to these mappings, more from the standpoint of free boundary problems.
(with A. Figalli, A. Guerra and H. Shahgholian) Constraint maps with free boundaries: the Bernoulli case, arXiv:2311.03006, 2023
(with K. Nyström) Higher order interpolative geometries and gradient regularity in evolutionary obstacle problems, arXiv: 2308.15818, 2023
(with A. Figalli and H. Shahgholian) Constraint maps with free boundaries: the obstacle case, arXiv:2302.07870, 2023.
(with H. Shahgholian) Almost minimizers to a transmission problem for (p,q) -Laplacian, arXiv:2301.08624, 2023
Please contact the directory administrator for the organization (department or similar) to correct possible errors in the information.