Semi-linear boundary problems of composition type in $L_p$-related spaces

Abstract

The class of problems treated here are elliptic partial differential equations with a homogeneous boundary condition and a non-linear perturbation obtained by composition with a fixed smooth function. The existence of solutions is obtained from the Leray--Schauder theorem or under a Landesman--Lazer condition on the data. Existence is carried over to a wide range of $L_p$-Sobolev spaces, using a non-trivial procedure to obtain a general regularity result. In fact the results are obtained in the general scales of Besov and Triebel--Lizorkin spaces.

arXiv comment41 pages. Accepted version. Published in 1997 by Marcel Dekker Inc., available at http://dx.doi.org/10.1080/03605309708821301

References in corpus (1)

• Pointwise multiplication of Besov and Triebel--Lizorkin spaces