Abstract
This paper is a continuation of the work begun in [6] on superposition operators, (Ngu) (x) = g(u(x)), between two arbitrary Sobolev spaces. Sufficient conditions which ensure the well-definedness, the continuity and the validity of the higher-order chain rule for such operators are given in the supercritical case (see Remark 1.1). As a consequence of these properties, it is proved that Ng (Wm,p (Ω) ∩ W0k,p (Ω)) ⊂ W0l,q (Ω).
Keywords: Sobolev spaces; superposition operators; higher-order chain rule; homogeneous Dirichlet conditions
Received: 2013-01-18
Published Online: 2016-03-10
Published in Print: 2014-02-01
© 2016 by Advanced Nonlinear Studies, Inc.
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