Non-negative solutions of the evolution p-Laplacian equation. Initial traces and cauchy problem when 1&lt;p&lt;2

Benedetto, E. Di; Herrero, Miguel A.

doi:10.1007/bf00400111

Cited by 99 publications

(81 citation statements)

References 17 publications

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“…There is an analogy between (1.1) and (1.2) both in terms of results (regularity [6,8,13,15], extinction time [3, 6,13], growth conditions [8,20]) and techniques of proof. For example, when m > 1, the theory of an intrinsic Harnack inequality can be developed for (1.1) paralleling that of (1.2) for p > 2 (see [7]).…”

Section: The Main Resultsmentioning

confidence: 99%

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Harnack Estimates and Extinction Profile for Weak Solutions of Certain Singular Parabolic Equations

Dibenedetto¹,

Kwong²

1992

Transactions of the American Mathematical Society

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Abstract. We establish an intrinsic Harnack estimate for nonnegative weak solutions of the singular equation (1.1) below, for m in the optimal range ((N -2)+/N, 1). Intrinsic means that, due to the singularity, the space-time dimensions in the parabolic geometry must be rescaled by a factor determined by the solution itself. Consequences are, sharp supestimates on the solutions and decay rates as t approaches the extinction time. Analogous results are shown for p-laplacian type equations.

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Section: The Main Resultsmentioning

confidence: 99%

“…The initial datum is taken in the sense of Lf^R^). Uniqueness can be shown by a technique similar to the one in [8,10].…”

Section: The Lj^-estimatementioning

confidence: 99%

Harnack Estimates and Extinction Profile for Weak Solutions of Certain Singular Parabolic Equations

Dibenedetto¹,

Kwong²

1992

Transactions of the American Mathematical Society

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show abstract

“…Ohee [4,5] and M. M. Porzio [61have discussed tbe local boundedness and the condition (12) is afro needed (lxi the case A = 2 and 1 <p < 2, (12) coincides with that in [3j-[6jaud is sharp in such a case as prova! in [3], III.?). Qur argument is different from that given in [3]- [6] and is ay improvement of [1].…”

mentioning

confidence: 94%

“…in [3], III.?). Qur argument is different from that given in [3]- [6] and is ay improvement of [1]. The result of bounda!ness is needed in regarding regularit>' of selutiens.…”

mentioning

confidence: 94%