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.
2008
Pubblicato
Rilevanza internazionale
Articolo
Sì, ma tipo non specificato
Settore MAT/05 - ANALISI MATEMATICA
English
Elliptic equations; Elliptic systems; Finite energy solutions; Quadratic growth
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].
Boccardo, L; Orsina, L; Porretta, A
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2108/30889
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