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Minimizers to reaction-diffusion PDEs, Sobolev inequalities, and monomial weights
Ros Oton, Xavier
Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada I; Cabré Vilagut, Xavier
Premi Évarist Galois 2012, atorgat per la Societat Catalana de Matemàtiques.
Reaction-diffusion equations play a central role in PDE theory and its applications to other sciences. They also play an important role in geometric problems: the problem of prescribing a curvature on a manifold and parabolic flows on manifolds. The aim of this project is the study of the regularity of minimizers to reaction-diffusion equations in certain doimains with symmetries and, as a consequence of it, some new Sobolev inequalities with monomial weights.. Reaction-diffusion equations play a central role in PDE theory and its applications to other sciences. They also play an important role in geometric problems: the problem of prescribing a curvature on a manifold and parabolic flows on manifolds. The aim of this project is the study of the regularity of minimizers to reaction-diffusion equations in certain doimains with symmetries and, as a consequence of it, some new Sobolev inequalities with monomial weights
Award-winning
Àrees temàtiques de la UPC::Matemàtiques i estadística::Equacions diferencials i integrals::Equacions en derivades parcials
Differential equations, Elliptic
extremal solution
sobolev inequalities
extremal solution
Equacions diferencials el·líptiques
Classificació AMS::35 Partial differential equations::35J Partial differential equations of elliptic type
info:eu-repo/semantics/masterThesis
Universitat Politècnica de Catalunya
         

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