Superposition with subunitary powers in Sobolev spaces
Résumé
Let 0 < a < 1 and set \Phi (t) = |t|^a, t\in R. Let 1 < p < \infty. We prove
that the superposition operator u \mapsto \Phi (u) maps the Sobolev space W^{1, p}(R^n) into the fractional
Sobolev space W^{a,p/a}(R^n). We also investigate the case of more general nonlinearities.
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