A Uniqueness Result for Quasilinear Elliptic Equations with Measures as Data
Jérôme Droniou, Thierry Gallouët · 2001
We prove here a uniqueness result for Solutions Obtained as the Limit of Approximations of quasilinear elliptic equations with different kinds of boundary conditions and measures as data. 1 Introduction 1.1 Notations In this paper,\\Omega is a bounded domain in R N (N 2), with a Lipschitz continuous boundary. The unit normal to @\\Omega outward to\\Omega is denoted by n. We denote by x \\Delta y the usual Euclidean product of two vectors (x; y) 2 R N \\Theta R N ; the associated Euclidean norm is written j:j. The Lebesgue measure of a measurable subset E in R N is denoted by jEj; oe is the Lebesgue measure on @\\Omega (i.e. the (N\\Gamma1)-dimensional Hausdorff measure). \\Gamma d and \\Gamma f are measurable subsets of @\\Omega such that @\\Omega = \\Gamma d [ \\Gamma f and oe(\\Gamma d " \\Gamma f ) = 0. For q 2 [1; +1], we denote by q 0 the conjugate exponent of q (i.e. q 0 = q=(q \\Gamma 1)). W 1;q is the usual Sobolev space, endowed with the norm jjujj W 1;q (\\Omega\\Gamm...