Geodesic
On the Continuity of Solutions to Elliptic Equations with Variable Order of Nonlinearity
Informatics and Automation, Differential equations and dynamical systems, Tome 261 (2008), pp. 7-15

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

We study the $p$-Laplacian with variable exponent $p(x)$ bounded away from unity and infinity. We obtain a sufficient condition on $p(x)$ under which all solutions of the $p$-Laplace equation are continuous at a fixed point of a domain, and find an estimate for the modulus of continuity of solutions. 
@article{TRSPY_2008_261_a0,
     author = {Yu. A. Alkhutov and O. V. Krasheninnikova},
     title = {On the {Continuity} of {Solutions} to {Elliptic} {Equations} with {Variable} {Order} of {Nonlinearity}},
     journal = {Informatics and Automation},
     pages = {7--15},
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     volume = {261},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TRSPY_2008_261_a0/}
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Yu. A. Alkhutov; O. V. Krasheninnikova. On the Continuity of Solutions to Elliptic Equations with Variable Order of Nonlinearity. Informatics and Automation, Differential equations and dynamical systems, Tome 261 (2008), pp. 7-15. http://geodesic.mathdoc.fr/item/TRSPY_2008_261_a0/