The one phase free boundary problem for the p-Laplacian with non-constant Bernoulli boundary condition
2002 (English)In: Transactions of the American Mathematical Society, ISSN 0002-9947, E-ISSN 1088-6850, Vol. 354, no 6, 2399-2416 p.Article in journal (Refereed) Published
Our objective, here, is to generalize our earlier results on the existence of classical convex solution to a free boundary problem with a Bernoulli-type boundary gradient condition and with the p-Laplacian as the governing operator. The main theorems of this paper assert that the exterior and the interior free boundary problem with a Bernoulli law, i.e. with a prescribed pressure a(x) on the free streamline of the flow, have convex solutions provided the initial domains are convex. The continuous function a(x) is subject to certain convexity properties. In our earlier results we have considered the case of constant a(x). In the lines of the proof of the main results we also prove the semi-continuity (up to the boundary) of the gradient of the p-capacitary potentials in convex rings, with C-1 boundaries.
Place, publisher, year, edition, pages
2002. Vol. 354, no 6, 2399-2416 p.
free boundary, convexity, non-linear joining conditions, classical-solutions, elliptic-equations, potential-theory, existence, regularity, operator, domains, points
IdentifiersURN: urn:nbn:se:kth:diva-21362ISI: 000174209700012OAI: oai:DiVA.org:kth-21362DiVA: diva2:340060
QC 201005252010-08-102010-08-10Bibliographically approved