Hölder regularity for solutions to complex Monge-Ampère equations

Mohamad Charabati

Annales Polonici Mathematici (2015)

  • Volume: 113, Issue: 2, page 109-127
  • ISSN: 0066-2216

Abstract

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We consider the Dirichlet problem for the complex Monge-Ampère equation in a bounded strongly hyperconvex Lipschitz domain in ℂⁿ. We first give a sharp estimate on the modulus of continuity of the solution when the boundary data is continuous and the right hand side has a continuous density. Then we consider the case when the boundary value function is 1 , 1 and the right hand side has a density in L p ( Ω ) for some p > 1, and prove the Hölder continuity of the solution.

How to cite

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Mohamad Charabati. "Hölder regularity for solutions to complex Monge-Ampère equations." Annales Polonici Mathematici 113.2 (2015): 109-127. <http://eudml.org/doc/286549>.

@article{MohamadCharabati2015,
abstract = {We consider the Dirichlet problem for the complex Monge-Ampère equation in a bounded strongly hyperconvex Lipschitz domain in ℂⁿ. We first give a sharp estimate on the modulus of continuity of the solution when the boundary data is continuous and the right hand side has a continuous density. Then we consider the case when the boundary value function is $^\{1,1\}$ and the right hand side has a density in $L^\{p\}(Ω)$ for some p > 1, and prove the Hölder continuity of the solution.},
author = {Mohamad Charabati},
journal = {Annales Polonici Mathematici},
keywords = {strongly hyperconvex Lipschitz domain; plurisubharmonic function; complex Monge-Ampère equation; modulus of continuity of solutions; Hölder continuity of solutions},
language = {eng},
number = {2},
pages = {109-127},
title = {Hölder regularity for solutions to complex Monge-Ampère equations},
url = {http://eudml.org/doc/286549},
volume = {113},
year = {2015},
}

TY - JOUR
AU - Mohamad Charabati
TI - Hölder regularity for solutions to complex Monge-Ampère equations
JO - Annales Polonici Mathematici
PY - 2015
VL - 113
IS - 2
SP - 109
EP - 127
AB - We consider the Dirichlet problem for the complex Monge-Ampère equation in a bounded strongly hyperconvex Lipschitz domain in ℂⁿ. We first give a sharp estimate on the modulus of continuity of the solution when the boundary data is continuous and the right hand side has a continuous density. Then we consider the case when the boundary value function is $^{1,1}$ and the right hand side has a density in $L^{p}(Ω)$ for some p > 1, and prove the Hölder continuity of the solution.
LA - eng
KW - strongly hyperconvex Lipschitz domain; plurisubharmonic function; complex Monge-Ampère equation; modulus of continuity of solutions; Hölder continuity of solutions
UR - http://eudml.org/doc/286549
ER -

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