Mathematical Sciences: Exterior Problems, Nonlinear Elasticity and Stochastic Evolution Problems

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This project has two parts. Part A involves work in nonlinear partial differential equations and the calculus of variations (Exterior Domain Problems, Prescribed Mean Curvature Problems and Perturbation of even Functionals, Lavrentiev gap, Lavrentiev envelope, homogeneous materials with layered microstructure, gradients with no rank-one connections). Part B deals with stochastic control and stochastic analysis (Bolza problems, Boundary value problems with noise, Kolmogorov differential equations). Most of these problems attempt to answer questions in engineering and physical sciences.