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},
     publisher = {mathdoc},
     volume = {261},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TRSPY_2008_261_a0/}
}
TY  - JOUR
AU  - Yu. A. Alkhutov
AU  - O. V. Krasheninnikova
TI  - On the Continuity of Solutions to Elliptic Equations with Variable Order of Nonlinearity
JO  - Informatics and Automation
PY  - 2008
SP  - 7
EP  - 15
VL  - 261
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TRSPY_2008_261_a0/
LA  - ru
ID  - TRSPY_2008_261_a0
ER  - 
%0 Journal Article
%A Yu. A. Alkhutov
%A O. V. Krasheninnikova
%T On the Continuity of Solutions to Elliptic Equations with Variable Order of Nonlinearity
%J Informatics and Automation
%D 2008
%P 7-15
%V 261
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TRSPY_2008_261_a0/
%G ru
%F TRSPY_2008_261_a0
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/

[1] Zhikov V. V., “Voprosy skhodimosti, dvoistvennosti i usredneniya dlya funktsionalov variatsionnogo ischisleniya”, Izv. AN SSSR. Ser. mat., 47:5 (1983), 961–998 | MR | Zbl

[2] Zhikov V. V., “Usrednenie funktsionalov variatsionnogo ischisleniya i teorii uprugosti”, Izv. AN SSSR. Ser. mat., 50:4 (1986), 675–710 | MR | Zbl

[3] Giaquinta M., “Growth conditions and regularity, a counterexample”, Manuscr. math., 59 (1987), 245–248 | DOI | MR | Zbl

[4] Marcellini P., Un exemple de solution discontinue d'un probléme variationell dans le cas scalaire, Preprint No 11, Inst. Mat. U. Dini. Univ. Firenze, 1987

[5] Růžička M., Electrorheological fluids: Modeling and mathematical theory, Lect. Notes Math., 1748, Springer, Berlin–New York, 2000 | MR

[6] Zhikov V. V., “On Lavrentiev's phenomenon”, Russ. J. Math. Phys., 3:2 (1995), 249–269 | MR | Zbl

[7] Ladyzhenskaya O. A., Uraltseva N. N., “Kvazilineinye ellipticheskie uravneniya i variatsionnye zadachi so mnogimi nezavisimymi peremennymi”, UMN, 16:1 (1961), 19–90 | MR | Zbl

[8] Marcellini P., “Regularity for elliptic equations with general growth conditions”, J. Diff. Equat., 105 (1993), 296–333 | DOI | MR | Zbl

[9] Fan X., Zhao D., “A class of De Giorgi type and Hölder continuity”, Nonlin. Anal. Theory Meth. and Appl., 36:3 (1999), 295–318 | DOI | MR | Zbl

[10] Alkhutov Yu. A., “Neravenstvo Kharnaka i gëlderovost reshenii nelineinykh ellipticheskikh uravnenii s nestandartnym usloviem rosta”, Dif. uravneniya, 33:12 (1997), 1651–1660 | MR | Zbl

[11] Chiadò Piat V., Coscia A., “Hölder continuity of minimizers of functionals with variable growth exponent”, Manuscr. math., 93 (1997), 283–299 | DOI | MR | Zbl

[12] Krasheninnikova O. V., “O nepreryvnosti v tochke reshenii ellipticheskikh uravnenii s nestandartnym usloviem rosta”, Tr. MIAN, 236, 2002, 204–211 | MR | Zbl

[13] Zhikov V. V., “O plotnosti gladkikh funktsii v prostranstve Soboleva–Orlicha”, Zap. nauch. sem. POMI, 310, 2004, 67–81 | MR | Zbl