Existence of <em>C</em><sup>1</sup>-solutions to Certain Non-uniformly Degenerate Elliptic Equations
Year: 1998
Journal of Partial Differential Equations, Vol. 11 (1998), Iss. 1 : pp. 9–24
Abstract
We are concerned with the Dirichlet problem of {div A(x, Du) + B(z) = 0 \qquad in Ω u= u_0 \qquad \qquad on ∂ Ω Here Ω ⊂ R^N is a bounded domain, A(x, p) = (A¹ (x, p), ... >A^N (x, p}) satisfies min{|p|^{1+α}, |p|^{1+β}} ≤ A(x, p) ⋅ p ≤ α_0(|p|^{1+α}+|p|^{1+β}) with 0 < α ≤ β. We show that if A is Lipschitz, B and u_0 are bounded and β < max {\frac{N+2}{N}α + \frac{2}{N},α + 2}, then there exists a C¹-weak solution of (0.1).
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/1998-JPDE-5551
Journal of Partial Differential Equations, Vol. 11 (1998), Iss. 1 : pp. 9–24
Published online: 1998-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 16
Keywords: Elliptic equation