Resumen de Perron's method and the method of relaxed limits for "unbounded" PDE in Hilbert spaces

Djivede Kelome, Andrzej Swiech

• We prove that Perron's method and the method of half-relaxed limits of Barles-Perthame works for the so called B-continuous viscosity solutions of a large class of fully nonlinear unbounded partiel differential equations in Hilbert spaces. Perron's method extends the existence of B-continuous viscosity solutions to many new equations that are not of Bellman type. The method of half-relaxed limits allows limiting operations with viscosity solutions without any a priori estimates. Possible applications of the method of half relaxed limits to large derivations, singular perturbation problems, and convergence of finite-dimensional approximations are discussed