, $\beta_1>0$, $0\leqslant \beta_2\leqslant p$, $\beta_1+\beta_2>p-1$, $\alpha>0$, sufficient conditions are given for removability of singular sets of dimension $\alpha$. These conditions are nearly necessary, and are given by the formula $$ 0\leqslant \alpha <n-\frac{p\beta_1+\beta_2}{\beta_1+\beta_2+1-p}. $$
@article{SM_1995_81_1_a11,
author = {M. V. Tuvaev},
title = {On removable singular sets for quasilinear elliptic equations},
journal = {Sbornik. Mathematics},
pages = {229--234},
year = {1995},
volume = {81},
number = {1},
language = {en},
url = {http://geodesic.mathdoc.fr/item/SM_1995_81_1_a11/}
}
M. V. Tuvaev. On removable singular sets for quasilinear elliptic equations. Sbornik. Mathematics, Tome 81 (1995) no. 1, pp. 229-234. http://geodesic.mathdoc.fr/item/SM_1995_81_1_a11/
[1] Ladyzhenskaya O. A., Uraltseva N. N., Lineinye i kvazilineinye uravneniya ellipticheskogo tipa, Nauka, M., 1973 | MR
[2] Gilbarg D., Trudinger N., Ellipticheskie differentsialnye uravneniya s chastnymi proizvodnymi vtorogo poryadka, Nauka, M., 1989 | MR | Zbl
[3] Serrin J., “Isolated singularities of solutions of quasilinear equations”, Acta Math., 113 (1965), 219–240 | DOI | MR | Zbl
[4] Vazquer J. L., Veron L., “Removable singularities of some strongly nonlinear elliptic equations”, Manuscripta Math., 33 (1980), 129–144 | DOI | MR
[5] Kondratev V. A., Landis E. M., “Polulineinye uravneniya vtorogo poryadka s neotritsatelnoi kharakteristicheskoi formoi”, Matem. zametki, 44:4 (1988), 457–468 | MR | Zbl
[6] Kondratev V. A., Landis E. M., “O kachestvennykh svoistvakh reshenii odnogo nelineinogo uravneniya vtorogo poryadka”, Matem. sb., 135(177) (1988), 346–360 | MR | Zbl
[7] Chistyakov V. V., “O nekotorykh kachestvennykh svoistvakh reshenii nedivergentnogo polulineinogo parabolicheskogo uravneniya vtorogo poryadka”, UMN, 41:5 (1986), 199–200 | MR | Zbl
[8] Tuvaev M. V., “Ob ustranimykh osobykh mnozhestvakh dlya polulineinykh ellipticheskikh i parabolicheskikh uravnenii”, Differents. uravneniya, 1990, no. 8, 1388–1396 | MR | Zbl
[9] Tuvaev M. V., “Ustranimye osobye mnozhestva dlya nelineinykh ellipticheskikh uravnenii”, Vestn. MGU. Ser. 1. Matem., mekh., 1992, no. 1, 8–13 | MR