Geodesic
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. 
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     title = {Continuity at {a~Point} for {Solutions} to {Elliptic} {Equations} with {a~Nonstandard} {Growth} {Condition}},
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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/

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