We establish the intrinsic Harnack inequality for nonnegative solutions of the parabolic p-Laplacian equation by a proof that uses neither the comparison principle nor explicit self-similar solutions. The significance is that the proof applies to quasilinear p-Laplacian-type equations, thereby solving a long-standing problem in the theory of degenerate parabolic equations.
Intrinsic Harnack estimates for nonnegative local solutions of degenerate parabolic equations / E. DIBENEDETTO; U. GIANAZZA; V. VESPRI. - In: ELECTRONIC RESEARCH ANNOUNCEMENTS OF THE AMERICAN MATHEMATICAL SOCIETY. - ISSN 1079-6762. - STAMPA. - 12:(2006), pp. 95-99. [10.1090/S1079-6762-06-00166-1]
Intrinsic Harnack estimates for nonnegative local solutions of degenerate parabolic equations
VESPRI, VINCENZO
2006
Abstract
We establish the intrinsic Harnack inequality for nonnegative solutions of the parabolic p-Laplacian equation by a proof that uses neither the comparison principle nor explicit self-similar solutions. The significance is that the proof applies to quasilinear p-Laplacian-type equations, thereby solving a long-standing problem in the theory of degenerate parabolic equations.File | Dimensione | Formato | |
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