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A doubly nonlinear evolution for the optimal Poincare inequality
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).ORCID iD: 0000-0003-4309-9242
2016 (English)In: Calculus of Variations and Partial Differential Equations, ISSN 0944-2669, E-ISSN 1432-0835, Vol. 55, no 4, 100Article in journal (Refereed) Published
Abstract [en]

We study the large time behavior of solutions of the PDE vertical bar v(t)vertical bar(p-2)v(t) = Delta(p)v. A special property of this equation is that the Rayleigh quotient integral(Omega) vertical bar Dv(x,t)vertical bar(p) dx/integral(Omega) vertical bar v(x,t)vertical bar(p) dx is nonincreasing in time along solutions. As t tends to infinity, this ratio converges to the optimal constant in Poincare's inequality. Moreover, appropriately scaled solutions converge to a function for which equality holds in this inequality. An interesting limiting equation also arises when p tends to infinity, which provides a new approach to approximating ground states of the infinity Laplacian.

Place, publisher, year, edition, pages
Springer, 2016. Vol. 55, no 4, 100
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-192741DOI: 10.1007/s00526-016-1026-3ISI: 000381989700029Scopus ID: 2-s2.0-84979674756OAI: oai:DiVA.org:kth-192741DiVA: diva2:974386
Note

QC 20160926

Available from: 2016-09-26 Created: 2016-09-20 Last updated: 2017-11-21Bibliographically approved

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