On removable singular sets for quasilinear elliptic equations
Sbornik. Mathematics, Tome 81 (1995) no. 1, pp. 229-234 Cet article a éte moissonné depuis la source Math-Net.Ru

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For equations of the form $$ \operatorname{div}(|\nabla u|^{p-2}\nabla u) =\alpha|u|^{\beta_1}|\nabla u|^{\beta_2}\operatorname{sgn}u,\qquad x\in\Omega\subset\mathbb{R}^n, $$ in the case $1, $\beta_1>0$, $0\leqslant \beta_2\leqslant p$, $\beta_1+\beta_2>p-1$, $\alpha>0$, sufficient conditions are given for removability of singular sets of dimension $\alpha$. These conditions are nearly necessary, and are given by the formula $$ 0\leqslant \alpha <n-\frac{p\beta_1+\beta_2}{\beta_1+\beta_2+1-p}. $$
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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