Weak solutions of some quasilinear elliptic equations with data measures. (English) Zbl 0809.35021

Alaa, Nour Eddine; Pierre, Michel

SIAM J. Math. Anal. 24, No. 1, 23-35 (1993).

Summary: Existence and uniqueness of weak solutions for some quasilinear elliptic equations with data measures and arbitrary growth with respect to the gradient are studied. Usual techniques based on a priori \(L^ \infty\)- bounds for the solutions and its gradient do not apply so that a new approach is needed. Various necessary and sufficient conditions are obtained on the data for existence. Relationship between existence of supersolutions and solutions is considered. Finally, sharp uniqueness results for weak solutions are given.

MSC:

35J65	Nonlinear boundary value problems for linear elliptic equations
35J25	Boundary value problems for second-order elliptic equations
35R05	PDEs with low regular coefficients and/or low regular data
35A05	General existence and uniqueness theorems (PDE) (MSC2000)

Keywords:

measure valued right hand side; quasilinear elliptic equations