Fully Nonlinear, Uniformly Elliptic Equations Under Natural Structure Conditions
نویسندگان
چکیده
منابع مشابه
Solvability of uniformly elliptic fully nonlinear PDE
We get existence, uniqueness and non-uniqueness of viscosity solutions of uniformly elliptic fully nonlinear equations of Hamilton-Jacobi-BellmanIsaacs type, with unbounded ingredients and quadratic growth in the gradient, without hypotheses of convexity or properness. Some of our results are new even for equations in divergence form.
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There has been much work on conformally invariant fully nonlinear elliptic equations and applications to geometry and topology. See for instance [17], [5], [4], [10], [14], [9], and the references therein. An important issue in the study of such equations is to classify entire solutions which arise from rescaling blowing up solutions. Liouville type theorems for general conformally invariant fu...
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Investigating for interior regularity of viscosity solutions to the fully nonlinear elliptic equation F (x, u,▽u,▽u) = 0, we establish the interior C continuity under the assumptions that F is uniformly elliptic, Hölder continuous and satisfies the natural structure conditions of fractional order, but without the concavity assumption of F . These assumptions are weaker and the result is stronge...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1983
ISSN: 0002-9947
DOI: 10.2307/1999182