In this paper, we are going to study the following elliptic system: {-div (b(x, z)del u) = f(x) in Omega, -div(a(x, z)del z) = b(x, z)vertical bar del u vertical bar(2) in Omega, u = 0, z = 0 on partial derivative Omega, where Omega is a bounded open subset of R-N, a(x, s) and b(x, s) are positive and coercive Caratheodory functions, and f is an element of L-m(Omega). The main purpose of this paper is to prove existence and regularity results with an improved regularity of the function z in the class of Sobolev spaces, and the existence of solutions (u, z) both with finite energy.
Boccardo, L., Orsina, L., Porretta, A. (2008). Existence of finite energy solutions for elliptic systems with L-1-valued nonlinearities. MATHEMATICAL MODELS AND METHODS IN APPLIED SCIENCES, 18(5), 669-687 [10.1142/S0218202508002814].
Existence of finite energy solutions for elliptic systems with L-1-valued nonlinearities
PORRETTA, ALESSIO
2008-01-01
Abstract
In this paper, we are going to study the following elliptic system: {-div (b(x, z)del u) = f(x) in Omega, -div(a(x, z)del z) = b(x, z)vertical bar del u vertical bar(2) in Omega, u = 0, z = 0 on partial derivative Omega, where Omega is a bounded open subset of R-N, a(x, s) and b(x, s) are positive and coercive Caratheodory functions, and f is an element of L-m(Omega). The main purpose of this paper is to prove existence and regularity results with an improved regularity of the function z in the class of Sobolev spaces, and the existence of solutions (u, z) both with finite energy.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.