# zbMATH — the first resource for mathematics

Prescribed singular submanifolds of some quasilinear elliptic equations. (English) Zbl 0947.35059
Quasilinear elliptic equations of special kind are considered. A concept of singular submanifolds for such equations is introduced. The existence and uniqueness of solutions for some quasilinear elliptic equations with singular submanifolds are investigated. The existence and uniqueness are studied for functions wich satisfy $$u(x) \to +\infty$$, $$\delta \to 0$$, where $$\delta$$ denotes the Euclidean distance from $$x$$ to the singular submanifolds.

##### MSC:
 35J60 Nonlinear elliptic equations 35A05 General existence and uniqueness theorems (PDE) (MSC2000)
Full Text:
##### References:
 [1] Vazquez, J.L.; Véron, L., Removable singularities of some strongly nonlinear elliptic equations, Manuscripta math., 33, 129-144, (1980) · Zbl 0452.35034 [2] Baras, P.; Pierre, M., Singularités éliminables pour des équations semi-linéaires, Ann. inst. Fourier, 34, 185-206, (1984) · Zbl 0519.35002 [3] Véron, L., Singularités éliminables d’équations elliptiques non liéaires, J. differential equations, 41, 87-95, (1981) · Zbl 0431.35005 [4] Grillot, M., Solutions singulières sur une sous-variété d’équations elliptiques non linéaires, C.R. acad. sci., 322, 49-54, (1996) · Zbl 0838.35036 [5] M. Grillot, Solutions of some nonlinear elliptic problems, which are singular on a submanifold, to appear. · Zbl 0897.35027 [6] Friedman, A.; Veron, L., Singular solutions of some quasilinear elliptic equations, Arch. rat. mech. anal., 96, 359-387, (1986) · Zbl 0619.35045 [7] L. Véron, Weak and strong singularities of nonlinear elliptic equations, Proceed. Symp. Pure Math. 45, part 2 (1986) 477-495. [8] C. Loewner, L. Nirenberg, Partial differential equations invariant under conformal or projective transformations, Contributions to Analysis, Academic Press, New York, 1974, pp. 245-272. · Zbl 0298.35018 [9] Bandle, C.; Marcus, M., Large solutions of semilinear elliptic equations: existence, uniqueness and asymptotic behaviour, J. analyse math., 58, 9-24, (1992) · Zbl 0802.35038 [10] Veron, L., Semilinear elliptic equations with uniform blowup on the boundary, J. anal. math., 59, 231-250, (1992) · Zbl 0802.35042 [11] Vazquez, J.L., An a priori interior estimate for the solutions of a nonlinear problem representing weak diffusion, Nonlinear anal., 5, 95-103, (1981) · Zbl 0446.35018 [12] Ratto, A.; Rigoli, M., L. Véron, scalar curvature and conformal deformations of hyperbolic space, J. funct. analysis, 121, 15-77, (1994) [13] Tolksdorf, P., Regularity for more general class of quasilinear elliptic equations, J. diff. equ., 51, 126-150, (1984) · Zbl 0488.35017
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.