Displaying similar documents to “Univalent solutions of elliptic systems of Heinz-Lewy type”

On Hölder regularity for elliptic equations of non-divergence type in the plane

Albert Baernstein II, Leonid V. Kovalev (2005)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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This paper is concerned with strong solutions of uniformly elliptic equations of non-divergence type in the plane. First, we use the notion of quasiregular gradient mappings to improve Morrey’s theorem on the Hölder continuity of gradients of solutions. Then we show that the Gilbarg-Serrin equation does not produce the optimal Hölder exponent in the considered class of equations. Finally, we propose a conjecture for the best possible exponent and prove it under an additional restriction. ...

Fully nonlinear second order elliptic equations with large zeroth order coefficient

L. C. Evans, Pierre-Louis Lions (1981)

Annales de l'institut Fourier

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We prove the existence of classical solutions to certain fully non-linear second order elliptic equations with large zeroth order coefficient. The principal tool is an estimate asserting that the C 2 , α -norm of the solution cannot lie in a certain interval of the positive real axis.