Tid: 8 juni 2015 kl 15.15-16.00.

Föredragshållare: Niklas Lundström

Titel: Viscosity solutions of oblique derivative problems for nonlinear parabolic PDEs in time-dependent domains

Abstract We prove existence and uniqueness of solutions to oblique derivative problems for fully nonlinear second-order parabolic pdes on non-smooth time-dependent domains. In particular, using standard theory of viscosity solutions together with construction of nontrivial test functions, we first prove a comparison principle. Armed with the comparison principle we prove existence through Perron's method and construction of several explicit viscosity sub and supersolutions. Our results are generalizations of a paper by Dupuis and Ishii to the setting of parabolic pdes and time-dependent domains.

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