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

Abstract

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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.

How to cite

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Baernstein 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 -

References

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