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  5. Rendiconti dell'Istituto di Matematica dell'Università di Trieste: an International Journal of Mathematics vol.29 (1997)
  6. Estimates and existence theorems for a class of nonlinear degenerate elliptic equations
 
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Estimates and existence theorems for a class of nonlinear degenerate elliptic equations

Esposito, V.
1997
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ISSN
0049-4704
http://hdl.handle.net/10077/4375
  • Article

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.
Series
Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics
29 (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.
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