A doubly nonlinear evolution for the optimal Poincare inequality
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
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
IdentifiersURN: urn:nbn:se:kth:diva-192741DOI: 10.1007/s00526-016-1026-3ISI: 000381989700029ScopusID: 2-s2.0-84979674756OAI: oai:DiVA.org:kth-192741DiVA: diva2:974386
QC 201609262016-09-262016-09-202016-09-26Bibliographically approved