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

Albert Baernstein II^{[1]}; Leonid V. Kovalev^{[1]}

- [1] Department of Mathematics Washington University Saint Louis, Missouri 63130, USA

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (2005)

- Volume: 4, Issue: 2, page 295-317
- ISSN: 0391-173X

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topBaernstein II, Albert, and Kovalev, Leonid V.. "On Hölder regularity for elliptic equations of non-divergence type in the plane." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 4.2 (2005): 295-317. <http://eudml.org/doc/84561>.

@article{BaernsteinII2005,

abstract = {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.},

affiliation = {Department of Mathematics Washington University Saint Louis, Missouri 63130, USA; Department of Mathematics Washington University Saint Louis, Missouri 63130, USA},

author = {Baernstein II, Albert, Kovalev, Leonid V.},

journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},

language = {eng},

number = {2},

pages = {295-317},

publisher = {Scuola Normale Superiore, Pisa},

title = {On Hölder regularity for elliptic equations of non-divergence type in the plane},

url = {http://eudml.org/doc/84561},

volume = {4},

year = {2005},

}

TY - JOUR

AU - Baernstein II, Albert

AU - Kovalev, Leonid V.

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

JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

PY - 2005

PB - Scuola Normale Superiore, Pisa

VL - 4

IS - 2

SP - 295

EP - 317

AB - 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.

LA - eng

UR - http://eudml.org/doc/84561

ER -

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