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Transactions of the American Mathematical Society

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Smoothness up to the boundary for solutions of the nonlinear and nonelliptic Dirichlet problem


Authors: C. J. Xu and C. Zuily
Journal: Trans. Amer. Math. Soc. 308 (1988), 243-257
MSC: Primary 35B65; Secondary 35D10, 35J60
DOI: https://doi.org/10.1090/S0002-9947-1988-0946441-4
MathSciNet review: 946441
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Abstract: For the Dirichlet problem associated with a general real second order p.d.e. $ F(x,\,u,\,\nabla u,\,{\nabla ^2}u) = 0$ in a smooth open set $ \Omega $ of $ {{\mathbf{R}}^n}$, we prove smoothness up to the boundary of the solution $ u$ for which the linearized characteristic form is nonnegative and satisfies Hörmander's brackets condition, the boundary of $ \Omega $ being noncharacteristic.


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DOI: https://doi.org/10.1090/S0002-9947-1988-0946441-4
Article copyright: © Copyright 1988 American Mathematical Society

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