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Regularity of Solutions for the Generalized Inhomogeneous Neumann Boundary Value Problem

✍ Scribed by T.R. Cranny

Publisher
Elsevier Science
Year
1996
Tongue
English
Weight
424 KB
Volume
126
Category
Article
ISSN
0022-0396

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✦ Synopsis

We describe regularity results for viscosity solutions of a fully nonlinear (possible degenerate) second-order elliptic PDE with inhomogeneous Neumann boundary condition holding in the generalized sense. These results only require that 0 is uniformly convex, 0 # C 1, / for some / # (0, 1) and that the differential operators satisfy mild regularity constraints such as Ho lder continuity.

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## Abstract The existence and uniqueness of the global generalized solution and the global classical solution to the initial boundary value problem for a system of generalized IMBq equations are proved. This paper also arrives at some sufficient conditions of blow up of the solution in finite tim