Displaying similar documents to “Viscosity solutions of the Cauchy problem for second-order nonlinear partial differential equations in Hilbert spaces.”

Viscosity subsolutions and supersolutions for non-uniformly and degenerate elliptic equations

Aris S. Tersenov (2009)

Archivum Mathematicum

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In the present paper we study the Dirichlet boundary value problem for quasilinear elliptic equations including non-uniformly and degenerate ones. In particular, we consider mean curvature equation and pseudo p-Laplace equation as well. It is well-known that the proof of the existence of continuous viscosity solutions is based on Ishii’s implementation of Perron’s method. In order to use this method one has to produce suitable subsolution and supersolution. Here we introduce new methods...