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Two-dimensional nonlinear boundary value problems for elliptic equations


Author: Gary M. Lieberman
Journal: Trans. Amer. Math. Soc. 300 (1987), 287-295
MSC: Primary 35J65; Secondary 35B65
DOI: https://doi.org/10.1090/S0002-9947-1987-0871676-8
MathSciNet review: 871676
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Abstract: Boundary regularity of solutions of the fully nonlinear boundary value problem

$\displaystyle F(x,u,Du,{D^2}u) = 0\quad {\text{in}}\;\Omega ,\qquad G(x,u,Du) = 0\quad {\text{on}}\;\partial \Omega $

is discussed for two-dimensional domains $ \Omega $. The function $ F$ is assumed uniformly elliptic and $ G$ is assumed to depend (in a nonvacuous manner) on $ Du$. Continuity estimates are proved for first and second derivatives of $ u$ under weak hypotheses for smoothness of $ F$, $ G$, and $ \Omega $.

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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1987-0871676-8
Keywords: Elliptic equations, boundary value problems, two-dimensional, boundary regularity
Article copyright: © Copyright 1987 American Mathematical Society

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