The Dirichlet problem and weighted spaces. II. (English) Zbl 0654.35039

Kufner, Alois; Opic, Bohumír

Čas. Pěstování Mat. 111, 242-253 (1986).

[For part I see ibid. 108, 381-408 (1983; Zbl 0589.35016).]
The paper is closely connected with Part I. First, it is shown how to use the results obtained in part I for elliptic differential operators which have strong singularities or which are strongly degenerated: it suffices to modify in an appropriate manner the definition of the weighted spaces used. Examples are given which illustrate the approach. The rest of the paper is devoted to an extension of the foregoing results to nonlinear elliptic operators: a class of such operators is described for which one can prove the existence of a weak solution of the Dirichlet problem in a given weighted Sobolev space.

MSC:

35J70	Degenerate elliptic equations
35J65	Nonlinear boundary value problems for linear elliptic equations
46E35	Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
35D05	Existence of generalized solutions of PDE (MSC2000)
35A20	Analyticity in context of PDEs

Keywords:

strong singularities; strongly degenerated; weighted spaces; existence; weak solution; Dirichlet problem; weighted Sobolev space

Citations:

Zbl 0589.35016