TY - JOUR
T1 - Existence of <em>C</em><sup>1</sup>-solutions to Certain Non-uniformly Degenerate Elliptic Equations
AU - Junjie Lee 
JO - Journal of Partial Differential Equations
VL - 1
SP - 9
EP - 24
PY - 1998
DA - 1998/11
SN - 11
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/jpde/5551.html
KW - Elliptic equation
KW - non-uniformly degenerate
AB -  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).