Geodesic
Continuity at a~Point for Solutions to Elliptic Equations with a~Nonstandard Growth Condition
Informatics and Automation, Differential equations and dynamical systems, Tome 236 (2002), pp. 204-211

Voir la notice de l'article provenant de la source Math-Net.Ru

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{TRSPY_2002_236_a20,
     author = {O. V. Krasheninnikova},
     title = {Continuity at {a~Point} for {Solutions} to {Elliptic} {Equations} with {a~Nonstandard} {Growth} {Condition}},
     journal = {Informatics and Automation},
     pages = {204--211},
     publisher = {mathdoc},
     volume = {236},
     year = {2002},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TRSPY_2002_236_a20/}
}
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O. V. Krasheninnikova. Continuity at a~Point for Solutions to Elliptic Equations with a~Nonstandard Growth Condition. Informatics and Automation, Differential equations and dynamical systems, Tome 236 (2002), pp. 204-211. http://geodesic.mathdoc.fr/item/TRSPY_2002_236_a20/