It is known that for any nonnegative function u compactly supported in R^n ∫(H(Du))^2 dx≥∫(H(Du^*))^2 dx where H is a nonnegative convex function, positively homogeneous of degree 1 and u^* is the "convex" rearrangement of u with respect to H. We deal with the problem of characterizing those functions u for which equality holds.

Convex rearrangement: equality cases in the Pòlya-Szegö inequality

VOLPICELLI, ROBERTA;
2004

Abstract

It is known that for any nonnegative function u compactly supported in R^n ∫(H(Du))^2 dx≥∫(H(Du^*))^2 dx where H is a nonnegative convex function, positively homogeneous of degree 1 and u^* is the "convex" rearrangement of u with respect to H. We deal with the problem of characterizing those functions u for which equality holds.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11588/8748
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