Abstract. Let Omega be a bounded convex open set of Rn; n greater or equal 2 with @Omega of class C^2,1: We consider the following Dirichlet problem 8< : u 2 H^2 \ H°^1 0( ;RN) F(x;D2u(x)) = f(x); a.e. in ; (0.1) where f 2 L2;( ;RN); n < n+2; F satises Campanato's Condition Ax and is Holder continuous in with exponent b: We show that there exist "; " 2 (0; 1); ("; " depend on and ), such that for any 2 (0; " n); and 2 (0; ]; with < (2b + ) ^ [ (n + 2)]; we have D2u 2 L2;( ;Rn2N); where " and " depend on the constants appearing in Condition Ax:
Regularity in Campanato Spaces for Solutions of Fully nonlinear Elliptic Systems
FATTORUSSO, Luisa Angela Maria;
2011-01-01
Abstract
Abstract. Let Omega be a bounded convex open set of Rn; n greater or equal 2 with @Omega of class C^2,1: We consider the following Dirichlet problem 8< : u 2 H^2 \ H°^1 0( ;RN) F(x;D2u(x)) = f(x); a.e. in ; (0.1) where f 2 L2;( ;RN); n < n+2; F satises Campanato's Condition Ax and is Holder continuous in with exponent b: We show that there exist "; " 2 (0; 1); ("; " depend on and ), such that for any 2 (0; " n); and 2 (0; ]; with < (2b + ) ^ [ (n + 2)]; we have D2u 2 L2;( ;Rn2N); where " and " depend on the constants appearing in Condition Ax:File in questo prodotto:
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