Geometric and Analytic Techniques in Calculus of Variations and Partial Differential Equations

1 June 2012 - 31 July 2012

Research Directions

IMPORTANT INFORMATION For each week of June there will be 30 grants for PhD students and young researchers interested to attend one or more schools. For each workshop to be held in July there will be also 20 grants for PhD students and young researchers. Please find here information about financial support and the registration form (which is needed for all participants).

AIMS AND DIRECTIONS The intensive period will last two months, June-July 2012 and will concentrate on the following topics: Quantitative geometric and functional inequalities with applications to the stability of solutions of variational problems and elliptic differential equations. Existence and regularity of solutions to optimal shape problems. Shape optimization and its connections with geometric inequalities and spectral geometry . Bi-Sobolev mappings, mappings of finite distortion, mappings with or without the N-property. Extensions and approximations of bi-Sobolev mappings. Nonlinear elliptic and parabolic equations, slow and fast diffusion. Entropy methods and functional inequalities. Connections with geometry. Each week of June will be devoted to one of the above four topics, with mini-courses and invited seminars at a doctoral/post doctoral level. Seminars at a more specialized level will be organized in July. A more detailed scheme is available in Planned activities

Funded by: ERC Advanced Grant n.226234 ''Analytic Techniques for Geometric and Functional Inequalities'', ERC Starting Grant n.258685 ''Analysis of Optimal Sets and Optimal Constants'', and INdAM (Istituto Nazionale di Alta Matematica)