Escola de Altos Estudos: Free Boundary Problems - Luis Caffarelli - Class 1 скачать в хорошем качестве

Escola de Altos Estudos: Free Boundary Problems - Luis Caffarelli - Class 1

Escola de Altos Estudos: Free Boundary Problems Prof. Luis Caffarelli (Texas - Austin) Página: http://www.impa.br/opencms/pt/ensino/... Download dos vídeos: http://video.impa.br/index.php?page=a... Free Boundary Problems: Common aspects and methods - Abstract : We will discuss several mathematical problems exhibiting the formation of free boundaries, and develop some tools and structures to approach them. Content: 1: Some basic tools: Properties of solutions to diffusion processes: second oreder equations in divergence and non divergence forms, variational and Perrons (viscosity methods) for second order equations. Interior and boundary Harnack inequalities for second order divergence equations. 2. a) The obstacle problem: optimal regularity and non degeneracy, blow up methods, free boundary regularity, similarities with the thery of boundary regularity for sets of minimal perimeter (minimal surfaces) b) Cavitation type problems: non-variational approach, minimal solutions, optimal regularity and non-degeneracy, a "Harnack inequality" approach: Lipschitz free boundaries are smooth. c) The Signorini problem (a non-local obstacle problem): Description of the problem, basic properties of the solution, regularity properties, some monotonicity properties, free boundary regularity. 3: Recapitulate, informal discussion of topics and problems. IMPA - Instituto Nacional de Matemática Pura e Aplicada © http://www.impa.br | http://video.impa.br     Os direitos sobre todo o material deste canal pertencem ao Instituto de Matemática Pura e Aplicada, sendo vedada a utilização total ou parcial do conteúdo sem autorização prévia e por escrito do referido titular, salvo nas hipóteses previstas na legislação vigente. The rights over all the material in this channel belong to the Instituto de Matemática Pura e Aplicada, and it is forbidden to use all or part of it without prior written authorization from the above mentioned holder, except in the cases prescribed in the current legislation.