C 1 , α regularity for elliptic equations with the general nonstandard growth conditions

Sungchol Kim; Dukman Ri

Mathematica Bohemica (2024)

  • Volume: 149, Issue: 3, page 365-396
  • ISSN: 0862-7959

Abstract

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We study elliptic equations with the general nonstandard growth conditions involving Lebesgue measurable functions on Ω . We prove the global C 1 , α regularity of bounded weak solutions of these equations with the Dirichlet boundary condition. Our results generalize the C 1 , α regularity results for the elliptic equations in divergence form not only in the variable exponent case but also in the constant exponent case.

How to cite

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Kim, Sungchol, and Ri, Dukman. "$C^{1,\alpha }$ regularity for elliptic equations with the general nonstandard growth conditions." Mathematica Bohemica 149.3 (2024): 365-396. <http://eudml.org/doc/299380>.

@article{Kim2024,
abstract = {We study elliptic equations with the general nonstandard growth conditions involving Lebesgue measurable functions on $\Omega $. We prove the global $C^\{1, \alpha \}$ regularity of bounded weak solutions of these equations with the Dirichlet boundary condition. Our results generalize the $C^\{1, \alpha \}$ regularity results for the elliptic equations in divergence form not only in the variable exponent case but also in the constant exponent case.},
author = {Kim, Sungchol, Ri, Dukman},
journal = {Mathematica Bohemica},
keywords = {nonstandard growth; $C^\{1, \alpha \}$ regularity; Hölder continuity; bounded weak solution; partial differential equations},
language = {eng},
number = {3},
pages = {365-396},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {$C^\{1,\alpha \}$ regularity for elliptic equations with the general nonstandard growth conditions},
url = {http://eudml.org/doc/299380},
volume = {149},
year = {2024},
}

TY - JOUR
AU - Kim, Sungchol
AU - Ri, Dukman
TI - $C^{1,\alpha }$ regularity for elliptic equations with the general nonstandard growth conditions
JO - Mathematica Bohemica
PY - 2024
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 149
IS - 3
SP - 365
EP - 396
AB - We study elliptic equations with the general nonstandard growth conditions involving Lebesgue measurable functions on $\Omega $. We prove the global $C^{1, \alpha }$ regularity of bounded weak solutions of these equations with the Dirichlet boundary condition. Our results generalize the $C^{1, \alpha }$ regularity results for the elliptic equations in divergence form not only in the variable exponent case but also in the constant exponent case.
LA - eng
KW - nonstandard growth; $C^{1, \alpha }$ regularity; Hölder continuity; bounded weak solution; partial differential equations
UR - http://eudml.org/doc/299380
ER -

References

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