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Estimates and existence theorems for a class of nonlinear degenerate elliptic equations
Esposito, V.
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.
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.
Languages
en
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