@Article{JPDE-11-1,
author = {},
title = {Existence of <em>C</em><sup>1</sup>-solutions to Certain Non-uniformly Degenerate Elliptic Equations},
journal = {Journal of Partial Differential Equations},
year = {1998},
volume = {11},
number = {1},
pages = {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), ... &gt;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 &lt; α ≤ β. We show that if A is Lipschitz, B and u_0 are bounded and β &lt; max {\frac{N+2}{N}α + \frac{2}{N},α + 2}, then there exists a C¹-weak solution of (0.1).},
issn = {2079-732X},
doi = {https://doi.org/1998-JPDE-5551},
url = {https://global-sci.com/article/88779/existence-of-emcemsup1sup-solutions-to-certain-non-uniformly-degenerate-elliptic-equations}
}