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Volume 11, Issue 1
Existence of C1-solutions to Certain Non-uniformly Degenerate Elliptic Equations

Junjie Lee

J. Part. Diff. Eq., 11 (1998), pp. 9-24.

Published online: 1998-11

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  • 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).
  • Keywords

Elliptic equation non-uniformly degenerate

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@Article{JPDE-11-9, author = {}, 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} }
TY - JOUR T1 - Existence of C1-solutions to Certain Non-uniformly Degenerate Elliptic Equations 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), ... >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).
Junjie Lee . (2019). Existence of C1-solutions to Certain Non-uniformly Degenerate Elliptic Equations. Journal of Partial Differential Equations. 11 (1). 9-24. doi:
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