Geodesic
Interior and boundary continuity of $p(x)$-harmonic functions
Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 49, Tome 508 (2021), pp. 7-38

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In this paper we establish results on interior and boundary continuity of $p(x)$-harmonic functions with discontinuous exponent $p(x)$. 
@article{ZNSL_2021_508_a0,
     author = {Yu. A. Alkhutov and M. D. Surnachev},
     title = {Interior and boundary continuity of $p(x)$-harmonic functions},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {7--38},
     publisher = {mathdoc},
     volume = {508},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2021_508_a0/}
}
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Yu. A. Alkhutov; M. D. Surnachev. Interior and boundary continuity of $p(x)$-harmonic functions. Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 49, Tome 508 (2021), pp. 7-38. http://geodesic.mathdoc.fr/item/ZNSL_2021_508_a0/