Strong solvability and uniqueness in Sobolev space are proved for the Dirichlet problem It is assumed that the coefficients of the quasilinear elliptic operator satisfy Carathéodory's condition, the a'i's are VMO functions with respect to x, and structure conditions on b are required. The main results are derived by means of the Aleksandrov-Pucci maximum principle and Leray-Schauder's fixed point theorem via a priori estimate for the L2n-norm of the gradient
Quasilinear elliptic equations with VMO coefficients / Palagachev, Dian Kostadinov. - In: TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY. - ISSN 0002-9947. - STAMPA. - 347:7(1995), pp. 2481-2493. [10.2307/2154833]
Quasilinear elliptic equations with VMO coefficients
Dian Kostadinov Palagachev
1995-01-01
Abstract
Strong solvability and uniqueness in Sobolev space are proved for the Dirichlet problem It is assumed that the coefficients of the quasilinear elliptic operator satisfy Carathéodory's condition, the a'i's are VMO functions with respect to x, and structure conditions on b are required. The main results are derived by means of the Aleksandrov-Pucci maximum principle and Leray-Schauder's fixed point theorem via a priori estimate for the L2n-norm of the gradientI documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
