A free-boundary problem for the evolution $p$-Laplacian equation with a combustion boundary condition

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dc.creatorTo, Tung
dc.date2007-11-20
dc.date.accessioned2026-07-07T08:43:56Z
dc.date.available2026-07-07T08:43:56Z
dc.descriptionWe study the existence, uniqueness and regularity of solutions of the equation $f_t = Δ_p f = \text{div} (|Df|^{p-2} Df)$ under over-determined boundary conditions $f = 0$ and $|Df| = 1$. We show that if the initial data is concave and Lipschitz with a bounded and convex support, then the problem admits a unique solution which exists until it vanishes identically. Furthermore, the free-boundary of the support of $f$ is smooth for all positive time.
dc.description25 pages, submitted
dc.identifierhttps://arxiv.org/abs/0711.3042
dc.identifierhttp://arxiv.org/abs/0711.3042
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/142488
dc.subjectAnalysis of PDEs
dc.subject35R35 (Primary); 35K55,35K65 (Secondary)
dc.titleA free-boundary problem for the evolution $p$-Laplacian equation with a combustion boundary condition
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