Non-convexity of level sets in convex rings for semilinear elliptic problems
2005 (English)In: Indiana University Mathematics Journal, ISSN 0022-2518, Vol. 54, no 2, 465-471 p.Article in journal (Refereed) Published
We show that there is a convex ring R = Omega(-) \ Q(+) C R-2 in which there exists a solution u to a semilinear partial differential equation Delta u = f(u), u = -1 on partial derivative Omega(-), u = 1 on partial derivative Omega(+), with level sets, not all convex. Moreover, every bounded solution u has at least one non-convex level set. In our construction, the nonlinearity f, is non-positive, and smooth.
Place, publisher, year, edition, pages
2005. Vol. 54, no 2, 465-471 p.
non-convexity, level set, semilinear elliptic equation, convex ring, singular perturbation problem, free-boundary problems, regular solutions, plasma physics, fluid-dynamics, equations, nonlinearities, existence, limit
IdentifiersURN: urn:nbn:se:kth:diva-14758ISI: 000229192400007ScopusID: 2-s2.0-20144376619OAI: oai:DiVA.org:kth-14758DiVA: diva2:332799
QC 201005252010-08-052010-08-05Bibliographically approved