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Estimates of solutions for the parabolic $p$-Laplacian equation with measure via parabolic nonlinear potentials

✍ Scribed by Liskevich, Vitali; Skrypnik, Igor I.; Sobol, Zeev

Book ID
118152560
Publisher
American Institute of Mathematical Sciences
Year
2012
Tongue
English
Weight
383 KB
Volume
12
Category
Article
ISSN
1534-0392

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## Abstract We study global solutions of u~t~=Ξ”__u__ + __f__(__u__, D__u__) with zero boundary data. Under suitable hypotheses on __f__, we show that an energy, which is roughly the __H__^1^ norm of __u__, cannot change too rapidly. When __f__ depends only on __u__, this estimate implies that all g