Continuity at a~Point for Solutions to Elliptic Equations with a~Nonstandard Growth Condition
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Differential equations and dynamical systems, Tome 236 (2002), pp. 204-211
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A question concerning the Hölder property of solutions to elliptic equations with a nonstandard growth condition is considered. The internal smoothness of solutions to an equation is proved at a fixed point under the condition that a variable exponent at this point has a logarithmic modulus of continuity. The proof is based on a modification of the Moser iteration technique.
@article{TM_2002_236_a20,
author = {O. V. Krasheninnikova},
title = {Continuity at {a~Point} for {Solutions} to {Elliptic} {Equations} with {a~Nonstandard} {Growth} {Condition}},
journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
pages = {204--211},
publisher = {mathdoc},
volume = {236},
year = {2002},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TM_2002_236_a20/}
}
TY - JOUR AU - O. V. Krasheninnikova TI - Continuity at a~Point for Solutions to Elliptic Equations with a~Nonstandard Growth Condition JO - Trudy Matematicheskogo Instituta imeni V.A. Steklova PY - 2002 SP - 204 EP - 211 VL - 236 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/TM_2002_236_a20/ LA - ru ID - TM_2002_236_a20 ER -
%0 Journal Article %A O. V. Krasheninnikova %T Continuity at a~Point for Solutions to Elliptic Equations with a~Nonstandard Growth Condition %J Trudy Matematicheskogo Instituta imeni V.A. Steklova %D 2002 %P 204-211 %V 236 %I mathdoc %U http://geodesic.mathdoc.fr/item/TM_2002_236_a20/ %G ru %F TM_2002_236_a20
O. V. Krasheninnikova. Continuity at a~Point for Solutions to Elliptic Equations with a~Nonstandard Growth Condition. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Differential equations and dynamical systems, Tome 236 (2002), pp. 204-211. http://geodesic.mathdoc.fr/item/TM_2002_236_a20/