Partial regularity for solutions of a nonlinear elliptic equation with singular nonlinearity |
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| Authors: | Zongming Guo Songbo Hou |
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| Affiliation: | aDepartment of Mathematics, Henan Normal University, Xinxiang 453002, PR China;bDepartment of Applied Mathematics, College of Science, East Campus, China Agricultural University, Beijing 100083, PR China |
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| Abstract: | We consider the following nonlinear elliptic equation with singular nonlinearity: where α>β>1, a>0, and Ω is an open subset of  , n 2. Let u H1(Ω) with  and  be a nonnegative stationary solution. If we denote the zero set of u by we shall prove that the Hausdorff dimension of Σ is less than or equal to  . |
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| Keywords: | Hausdorff dimension Singular nonlinearity Stationary solutions Zero set Monotonicity inequality |
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