Please use this identifier to cite or link to this item: http://hdl.handle.net/10077/4375
Title: Estimates and existence theorems for a class of nonlinear degenerate elliptic equations
Authors: Esposito, V.
Issue Date: 1997
Publisher: Università degli Studi di Trieste. Dipartimento di Scienze Matematiche
Source: V. Esposito, "Estimates and existence theorems for a class of nonlinear degenerate elliptic equations", in: Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics, 29 (1997), pp. 189-205.
Series/Report no.: Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics
29 (1997)
Abstract: Let $\left\{ a_{i,j}\left(x,\eta\right)\right\} $ be a matrix of bounded Carathéodory functions such that $a_{i,j}\left(x,\eta\right)\xi_{j},\xi_{i}\geq b\left(\mid\eta\mid\right)\nu\left(x\right)\mid\xi\mid^{2}\qquad\forall\xi\epsilon\mathbb{R^{\textrm{n}}},$ where b: $[0,+\infty[$$\rightarrow\mathbb{R}$ is a positive bounded continuous function and $\nu\epsilon L^{1},\frac{1}{\nu}\epsilon L^{t}$ with t >1. A priori estimates for solutions of the homogeneous Dirichlet problem related to the equation $-\left(a_{i,j}\left(x,u\right)u_{x_{j}}\right)_{x_{i}}=f$ are proved under various summability assumptions on f. As a consequence, existence theorems are obtained.
URI: http://hdl.handle.net/10077/4375
ISSN: 0049-4704
Appears in Collections:Rendiconti dell'Istituto di matematica dell'Università di Trieste: an International Journal of Mathematics vol.29 (1997)

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