Research

Currently I am working on different questions in partial differential equations (PDEs) including:

Free boundary problems, elliptic and non local PDEs.

Carleman estimates and quantitative uniqueness for waves.

Singular and low regularity solutions to equations in fluid mechanics.

Also, during my PhD I studied observability properties of geometric evolution equations via Carleman inequalities, conformally covariant operators and also certain models of shallow water waves with singular behavior. You can check out my thesis "Weighted inequalities in Fluid Mechanics and General Relativity" supervised by Alberto Enciso (CSIC-ICMAT).

Although the aforementioned problems arise in very different contexts, at some extent they share some basic analytical techniques to deal with singularities and often involve the study of non local operators.

Click here to get my CV with an updated list of publications and preprints:

Carleman inequalities for parabolic equations with inverse square potentials and boundary observability, with A. Enciso and A. Shao. In preparation (2020).

Carleman estimates with sharp weights and boundary observability for wave equations with critically singular potentials, with A. Enciso and A. Shao. JEMS, in press (2020).

Convexity of Whitham's highest cusped wave, with A. Enciso and J. Gómez-Serrano. ArXiv preprint:1810.10935. Submitted (2018).

Fractional powers of the wave operator via Dirichlet-to-Neumann maps in anti-de Sitter spaces, with A. Enciso and M. del Mar González. J. Funct. Anal. 273 2144-2166 (2017).

You can also obtain my preprints from arXiv or check out my Google Scholar profile