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A free boundary problem for infinity-Laplace equation
KTH, Superseded Departments, Mathematics.ORCID iD: 0000-0002-1316-7913
2002 (English)In: Calculus of Variations and Partial Differential Equations, ISSN 0944-2669, E-ISSN 1432-0835, Vol. 14, no 3, 359-384 p.Article in journal (Refereed) Published
Abstract [en]

We consider a free boundary problem for the p-Laplacian Delta(mu)u = div(\delu\(p-2)delu), describing nonlinear potential flow past a convex profile K with prescribed pressure \delu(x)\ = a(x) on the free stream line. The main purpose of this paper is to study the limit as p --> infinity of the classical solutions of the problem above, existing under certain convexity assumptions on a(x). We show, as one can expect, that the limit solves the corresponding potential flow problem for the infinity-Laplacian Deltax u = del(2) u delu . delu. in a certain weak sense, strong enough however, to guarantee uniqueness. We show also that in the special case a(x) = a(0) > 0 the limit is given by the distance function.

Place, publisher, year, edition, pages
2002. Vol. 14, no 3, 359-384 p.
Keyword [en]
elliptic-equations, regularity, existence, gradient
URN: urn:nbn:se:kth:diva-21548DOI: 10.1007/s005260100107ISI: 000175607800006OAI: diva2:340246
QC 20100525Available from: 2010-08-10 Created: 2010-08-10Bibliographically approved

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