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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. |
Type: | Article | 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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