A free boundary problem for the <i>p</i>-Laplacian: uniqueness, convexity, and successive approximation of solutions
classical solution of a Bernoulli-type free boundary problem for the $p$-Laplace equation, $ 1 < p < infty $. In addition, we prove the existence of a classical solution in $N$ dimensions when $p = 2$ and, for $ 1 < p < infty $, results on uniqueness and starlikeness of the free boundary...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Texas State University
1995-06-01
|
| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/1995/08/abstr.html |
| _version_ | 1818956935393705984 |
|---|---|
| author | A. Acker R. Meyer |
| author_facet | A. Acker R. Meyer |
| author_sort | A. Acker |
| collection | DOAJ |
| description | classical solution of a Bernoulli-type free boundary problem for the $p$-Laplace equation, $ 1 < p < infty $. In addition, we prove the existence of a classical solution in $N$ dimensions when $p = 2$ and, for $ 1 < p < infty $, 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 < infty $) that the free boundary is convex when the fixed boundary is convex. |
| first_indexed | 2024-12-20T11:01:51Z |
| format | Article |
| id | doaj.art-2bf43cfe3b9541acb1c51db48ef63c35 |
| institution | Directory Open Access Journal |
| issn | 1072-6691 |
| language | English |
| last_indexed | 2024-12-20T11:01:51Z |
| publishDate | 1995-06-01 |
| publisher | Texas State University |
| record_format | Article |
| series | Electronic Journal of Differential Equations |
| spelling | doaj.art-2bf43cfe3b9541acb1c51db48ef63c352022-12-21T19:43:00ZengTexas State UniversityElectronic Journal of Differential Equations1072-66911995-06-01199508120A free boundary problem for the <i>p</i>-Laplacian: uniqueness, convexity, and successive approximation of solutionsA. AckerR. Meyerclassical solution of a Bernoulli-type free boundary problem for the $p$-Laplace equation, $ 1 < p < infty $. In addition, we prove the existence of a classical solution in $N$ dimensions when $p = 2$ and, for $ 1 < p < infty $, 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 < infty $) that the free boundary is convex when the fixed boundary is convex.http://ejde.math.txstate.edu/Volumes/1995/08/abstr.htmlp-LaplaceFree boundaryApproximation of solutions. |
| spellingShingle | A. Acker R. Meyer A free boundary problem for the <i>p</i>-Laplacian: uniqueness, convexity, and successive approximation of solutions Electronic Journal of Differential Equations p-Laplace Free boundary Approximation of solutions. |
| title | A free boundary problem for the <i>p</i>-Laplacian: uniqueness, convexity, and successive approximation of solutions |
| title_full | A free boundary problem for the <i>p</i>-Laplacian: uniqueness, convexity, and successive approximation of solutions |
| title_fullStr | A free boundary problem for the <i>p</i>-Laplacian: uniqueness, convexity, and successive approximation of solutions |
| title_full_unstemmed | A free boundary problem for the <i>p</i>-Laplacian: uniqueness, convexity, and successive approximation of solutions |
| title_short | A free boundary problem for the <i>p</i>-Laplacian: uniqueness, convexity, and successive approximation of solutions |
| title_sort | free boundary problem for the i p i laplacian uniqueness convexity and successive approximation of solutions |
| topic | p-Laplace Free boundary Approximation of solutions. |
| url | http://ejde.math.txstate.edu/Volumes/1995/08/abstr.html |
| work_keys_str_mv | AT aacker afreeboundaryproblemfortheipilaplacianuniquenessconvexityandsuccessiveapproximationofsolutions AT rmeyer afreeboundaryproblemfortheipilaplacianuniquenessconvexityandsuccessiveapproximationofsolutions AT aacker freeboundaryproblemfortheipilaplacianuniquenessconvexityandsuccessiveapproximationofsolutions AT rmeyer freeboundaryproblemfortheipilaplacianuniquenessconvexityandsuccessiveapproximationofsolutions |