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On a nonlinear compactness lemma in $$L^{p}(0,T;B)$$. (English) Zbl 1032.46032
Summary: We consider a nonlinear counterpart of a compactness lemma of J. Simon [Ann. Mat. Pura Appl. (4) 146, 65-96 (1987; Zbl 0629.46031)], which arises naturally in the study of doubly nonlinear equations of elliptic-parabolic type. This paper was motivated by previous results of J. Simon (loc. cit.), recently sharpened by H. Amann [Glas. Mat., Ser. III 35, 161-177 (2000; Zbl 0997.46029)] in the linear setting, and by a nonlinear compactness argument of H. W. Alt and S. Luckhaus [Math. Z. 183, 311-341 (1983; Zbl 0497.35049)].

##### MSC:
 46B50 Compactness in Banach (or normed) spaces 47H30 Particular nonlinear operators (superposition, Hammerstein, Nemytskiĭ, Uryson, etc.) 46E40 Spaces of vector- and operator-valued functions 34G20 Nonlinear differential equations in abstract spaces 35K65 Degenerate parabolic equations
compactness
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