On quasilinear elliptic equations with fully nonlinear boundary conditions

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Venue:DM 409A

Abstract: We consider nonlinear elliptic partial differential equations subject to fully nonlinear boundary conditions involving boundary operators of the same order as the bulk operators. We discuss issues such as existence of bounded solutions and regularity. We illustrate the application of our results to a class of uniformly elliptic equations that occur in the theory of phase transitions of different materials, and certain elliptic systems associated with climate problems, which describe the evolution of atmospheric sea-level temperatures for relatively long time scales.