Joaquim Serra (mathematician)

Joaquim Serra Montolí (born October 20, 1986 in Barcelona ) is a Spanish mathematician .

Serra studied at the Polytechnic University of Catalonia (UPC) in Barcelona with a master's degree in 2010 and a doctorate with Xavier Cabré in 2014 (dissertation: Elliptic and parabolic PDEs: regularity for nonlocal diffusion equations and two isoperimetric problems ). As a post-doctoral student he went into industry (consultant at the Arcvi Big Data Agency ), was partly at the UPC, at the Weierstrass Institute for Applied Analysis and Stochastics in Berlin with Enrico Valdinoci and from 2016 at the ETH Zurich with Alessio Figalli . From 2018 he is an SNSF Ambizione Fellow at ETH Zurich.

He deals with regularity issues of elliptical and parabolic partial differential equations , reaction-diffusion equations , phase transitions , minimal areas , free boundary value problems and integro differential equations .

In 2016 he received the Josep Teixidó Prize of the Catalan Mathematical Society, in 2018 the Jose Luis Rubio de Francia Prize of the Royal Spanish Mathematical Society and in 2019 the Antonio Valle Prize of the Spanish Society of Applied Mathematics. For 2020/21 he received the EMS Prize .

Fonts (selection)

with Xavier Ros-Oton: The Dirichlet problem for the fractional Laplacian: regularity up to the boundary , Journal de Mathématiques Pures et Appliquées, Volume 101, 2014, pp. 275-302, Arxiv
with X. Ros-Oton: The Pohozaev identity for the fractional Laplacian , Archive for Rational Mechanics and Analysis, Volume 213, 2014, pp. 587–628, Arxiv
with X. Ros-Oton: The extremal solution for the fractional Laplacian , Calculus of Variations and Partial Differential Equations, Volume 50, 2014, pp. 723-750, Arxiv
Regularity for fully nonlinear nonlocal parabolic equations with rough kernels , Calculus of Variations and Partial Differential Equations, Volume 54, 2015, pp. 615–629, Arxiv
with X. Ros-Oton: Nonexistence results for nonlocal equations with critical and supercritical nonlinearities , Communications in Partial Differential Equations, Volume 40, 2015, pp. 115-133, Arxiv
with X. Ros-Oton: Regularity theory for general stable operators , Journal of Differential Equations, Volume 260, 2016, pp. 8675-8715, Arxiv
with X. Ros-Oton: Boundary regularity for fully nonlinear integro-differential equations, Duke Math. J., Volume 165, 2016, pp. 2079–2154. Arxiv
with S. di Pierro, E. Valdinoci: Improvement of flatness for nonlocal phase transitions,, appears in American Journal of Mathematics, Arxiv 2016
with A. Figalli: On stable solutions for boundary reactions: a De Giorgi type result in dimension 4 + 1, appears in Inventiones Mathematicae, Arxiv 2017
with Luis Caffarelli , X. Ros-Oton: Obstacle problems for integro-differential operators: regularity of solutions and free boundaries , Invent. Math., Volume 208, 2017, pp. 1155-1211. Arxiv
with A. Figalli, X. Ros-Oton: Generic regularity of free boundaries for the obstacle problem, Arxiv 2019
with X. Cabré, A. Figalli, X. Ros-Oton: Stable solutions to semilinear elliptic equations are smooth up to dimension 9 , Arxiv , 2019
with A. Figalli: On the fine structure of the free boundary for the classical obstacle problem , Invent. Math., Volume 215, 2019, pp. 311-366. Arxiv
with E. Cinti, E. Valdinoci: Quantitative flatness results and BV estimates for nonlocal minimal surfaces,, J. Differential Geom., Volume 112, 2019, pp. 447-504. Arxiv

Web links

Homepage, ETH Zurich

Individual evidence

personal data
SURNAME	Serra, Joaquim
ALTERNATIVE NAMES	Serra Montolí, Joaquim
BRIEF DESCRIPTION	Spanish mathematician
DATE OF BIRTH	October 20, 1986
PLACE OF BIRTH	Barcelona

[1] Joaquim Serra in the Mathematics Genealogy Project (English)

[2] Biography of the EMS Prize