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Boundary Lipschitz regularity of solutions for semilinear elliptic equations in divergence form

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 Added by Jingqi Liang
 Publication date 2021
  fields
and research's language is English




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In this paper, we consider the pointwise boundary Lipschitz regularity of solutions for the semilinear elliptic equations in divergence form mainly under some weaker assumptions on nonhomogeneous term and the boundary. If the domain satisfies C^{1,text{Dini}} condition at a boundary point, and the nonhomogeneous term satisfies Dini continuous condition and Lipschitz Newtonian potential condition, then the solution is Lipschitz continuous at this point. Furthermore, we generalize this result to Reifenberg C^{1,text{Dini}} domains.



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