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; A., Tarsia. - In: DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS. - ISSN 1078-0947. - A 31:4( Dic 2011)#17 special issue(2011), pp. 1307-1323. [doi:10.3934/dcds.2011.31.1307]
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:I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
