Existence and uniqueness for nonlinear elliptic equations with unbounded coefficients

Abstract We study the nonlinear Dirichlet problem for the elliptic equation div(A(x,∇u)+B(x,u))=divF%$\begin{aligned} \mathrm {div}\;(\fancyscript{A}(x,\nabla u)+\fancyscript{B}(x,u)) = \mathrm {div}\;F \end{aligned}%$in a regular domain %$\varOmega \subset \mathbb R^N%$, %$N>2%$. We assume that...
Ausführliche Beschreibung

Abstract We study the nonlinear Dirichlet problem for the elliptic equation div(A(x,∇u)+B(x,u))=divF%$\begin{aligned} \mathrm {div}\;(\fancyscript{A}(x,\nabla u)+\fancyscript{B}(x,u)) = \mathrm {div}\;F \end{aligned}%$in a regular domain %$\varOmega \subset \mathbb R^N%$, %$N>2%$. We assume that the growth coefficient of %$\fancyscript{A}(x,\xi )%$ is in the space of functions with bounded mean oscillation and the lower order term %$\fancyscript{B}(x,s)%$ satisfies |B(x,s)-B(x,t)|⩽b(x)|s-t|%$\begin{aligned} |\fancyscript{B}(x,s)- \fancyscript{B}(x,t) | \leqslant b(x)|s-t| \end{aligned}%$for a.e. %$x\in \varOmega %$ and for any %$s,t\in \mathbb R%$, where %$b%$ is a non negative function in the Lorentz space %$L^{N,q}(\varOmega ) %$, %$N\leqslant q\leqslant +\infty %$. If %$F \in L^p%$ and %$q<+\infty %$, we obtain existence and uniqueness for distributional solutions %$u \in W^{1,p}_0(\varOmega )%$ whenever %$p \geqslant 2%$. For %$q=+\infty %$ uniqueness of solutions in %$W^{1,2}_0(\varOmega )%$ is proved. Ausführliche Beschreibung

Autor*in:	Radice, Teresa [verfasserIn] Zecca, Gabriella

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2014

Schlagwörter:	Dirichlet problem Infinite energy solution Bounded mean oscillation

Anmerkung:	© Università degli Studi di Napoli "Federico II" 2014

Übergeordnetes Werk:	Enthalten in: Ricerche di matematica - Milano : Springer, 2006, 63(2014), 2 vom: 05. Aug., Seite 355-367
Übergeordnetes Werk:	volume:63 ; year:2014 ; number:2 ; day:05 ; month:08 ; pages:355-367

Links:	Volltext

DOI / URN:	10.1007/s11587-014-0202-z

Katalog-ID:	SPR02094571X