A note on regularity of solutions for degenerate singular elliptic boundary value problems |
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Authors: | D D Hai |
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Institution: | 1.Department of Mathematics and Statistics,Mississippi State University,Mississippi State,USA |
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Abstract: | We prove the \(C^{1,\beta }\)-boundary regularity and a comparison principle for weak solutions of the problem $$\begin{aligned} \left\{ \begin{array}{ll} -\Delta _{p}u-\lambda \psi _{p}(u)=f(x)&{}\quad \text {in }\Omega , \\ u=0&{}\quad \text {on }\partial \Omega , \end{array} \right. \end{aligned}$$ where \(\Omega \) is a bounded domain in \(\mathbb {R}^{N},N>1\ \)with smooth boundary \(\partial \Omega ,\ \ \Delta _{p}u=\mathrm{div}(|\nabla u|^{p-2}\nabla u),\psi _{p}(u)=|u|^{p-2}u,p>1,\ \)and f is allowed to be unbounded. |
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