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Existence of solutions for degenerate quasilinear elliptic equations

โœ Scribed by Weilin Zou; Fengquan Li

Publisher
Elsevier Science
Year
2010
Tongue
English
Weight
390 KB
Volume
73
Category
Article
ISSN
0362-546X

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โœฆ Synopsis

This paper deals with a class of degenerate quasilinear elliptic equations of the form -div(a(x, u, โˆ‡u) = gdiv(f ), where a(x, u, โˆ‡u) is allowed to be degenerate with the unknown u. We prove existence of bounded solutions under some hypothesis on f and g.

Moreover we prove that there exists a renormalized solution in the case where g โˆˆ L 1 (โ„ฆ) and f โˆˆ (L p (โ„ฆ)) N .

๐Ÿ“œ SIMILAR VOLUMES

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We prove the existence of bounded solutions of some boundary value problems for degenerate elliptic equations of second order in divergence form. Our results cover also the unbounded domain case. We discuss also the uniqueness problem and asymptotic behaviour of the solutions of our equation.