@Article{JPDE-11-9, author = {Junjie Lee }, title = {Existence of C¹-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), ... >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).}, issn = {2079-732X}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jpde/5551.html} }