Monotonicity of solutions of Fully nonlinear uniformly elliptic equations in the half-plane |
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| Authors: | F. Charro |
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| Affiliation: | a Department of Mathematics, The University of Texas, 1 University Station C1200, Austin, TX 78712, USA
b Dipartimento di Matematica, UNICAL, Ponte Pietro Bucci 31B, 87036 Arcavacata di Rende, Cosenza, Italy |
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| Abstract: | In this paper we study the monotonicity of positive (or non-negative) viscosity solutions to uniformly elliptic equations F(∇u,D2u)=f(u) in the half plane, where f is locally Lipschitz continuous (with f(0)?0) and zero Dirichlet boundary conditions are imposed. The result is obtained without assuming the u or |∇u| are bounded. |
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| Keywords: | 35J60 35B05 35B09 35B50 |
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