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dc.contributor.authorRos Oton, Xavier
dc.descriptionXavier Ros-Oton, ex-estudiant de la FME i doctor en Matemàtiques per la UPC (2014, premi Extraordinari de Doctorat), ha treballat a la University of Texas at Austin (USA, 2014-17), i actualment a la Universität Zürich (Suïssa). Com a investigador, treballa principalment en el camp de les Equacions en Derivades Parcials (EDP). L’any 2017 rebé el premi J. L. Rubio de Francia de la Real Sociedad Matemàtica Española (RSME), un dels premis més importants en matemàtiques a l’Estat espanyol. També el 2017, fou guardonat amb el premi Antonio Valle de la Sociedad Española de Matemática Aplicada (SeMA). Amb 29 anys, es convertí en el guanyador més jove d’aquest premi i en la primera persona a guanyar-los tots dos el mateix any.
dc.description.abstractFree boundary problems are those described by PDE's that exhibit a priori unknown (free) interfaces or boundaries. In other words, there are two unknowns in these problems: the solution of a PDE, and a free boundary which determines the domain in which the PDE is satisfied. Such type of problems appear in Physics, Probability, Biology, Finance, or Industry, and the study of solutions and free boundaries uses methods from PDE's, Calculus of Variations, and Geometric Measure Theory. The main mathematical challenge is understanding the regularity of free boundaries. The obstacle problem is the most classical and motivating example in the study of free boundary problems. A milestone in this context is a classical paper of L. Caffarelli (Acta Math. 1977), in which he established for the first time the regularity of free boundaries in the obstacle problem. This is one of the main results for which he got the Wolf Prize in 2012. The goal of this talk is to present and motivate different free boundary problems, explain the main known results in this context, and give an overview of the current research and open problems.
dc.rightsAttribution-NonCommercial-ShareAlike 3.0 Spain
dc.subjectÀrees temàtiques de la UPC::Matemàtiques i estadística::Equacions diferencials i integrals::Equacions diferencials ordinàries
dc.subject.lcshDifferential equations
dc.titleRegularity of free boundaries in obstacle problems
dc.subject.lemacEquacions diferencials ordinàries
dc.subject.amsClassificació AMS::34 Ordinary differential equations
dc.rights.accessOpen Access

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