A Free Boundary Problem for the p-Laplacian: Uniqueness, Convexity, and Successive Approximation of Solutions

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dc.contributor.authorAcker, Andrew F.
dc.contributor.authorMeyer, R.
dc.date.accessioned2018-08-21T16:29:16Z
dc.date.available2018-08-21T16:29:16Z
dc.date.issued1995-06-21
dc.description.abstractWe prove convergence of a trial free boundary method to a classical solution of a Bernoulli-type free boundary problem for the p-Laplace equation, 1 < p < ∞. In addition, we prove the existence of a classical solution in N dimensions when p = 2 and, for 1 < p < ∞, results on uniqueness and starlikeness of the free boundary and continuous dependence on the fixed boundary and on the free boundary data. Finally, as an application of the trial free boundary method, we prove (also for 1 < p < ∞) that the free boundary is convex when the fixed boundary is convex.
dc.description.departmentMathematics
dc.formatText
dc.format.extent20 pages
dc.format.medium1 file (.pdf)
dc.identifier.citationAcker, A. & Meyer, R. (1995). A free boundary problem for the p-Laplace: uniqueness, convexity, and successive approximation of solutions. Electronic Journal of Differential Equations, 1995(08), pp. 1-20.
dc.identifier.issn1072-6691
dc.identifier.urihttps://hdl.handle.net/10877/7566
dc.language.isoen
dc.publisherSouthwest Texas State University, Department of Mathematics
dc.rightsAttribution 4.0 International
dc.rights.holderThis work is licensed under a Creative Commons Attribution 4.0 International License.
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/
dc.sourceElectronic Journal of Differential Equations, 1995, San Marcos, Texas: Southwest Texas State University and University of North Texas.
dc.subjectp-Laplace
dc.subjectFree boundary
dc.subjectApproximation of solutions
dc.titleA Free Boundary Problem for the p-Laplacian: Uniqueness, Convexity, and Successive Approximation of Solutions
dc.typeArticle

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