Boundary monotonicity formulae and applications to free boundary problems I: The elliptic case
We derive a monotonicity formula at boundary points for a class of nonlinear elliptic partial differential equations, including the obstacle problem case, quenching, a free boundary problem with Bernoulli-type free boundary condition as well as the blow-up case. As application model we prove - for D...
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| Format: | Article |
| Language: | English |
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Texas State University
2004-03-01
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| Series: | Electronic Journal of Differential Equations |
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| Online Access: | http://ejde.math.txstate.edu/Volumes/2004/44/abstr.html |
| _version_ | 1828846275582230528 |
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| author | Georg S. Weiss |
| author_facet | Georg S. Weiss |
| author_sort | Georg S. Weiss |
| collection | DOAJ |
| description | We derive a monotonicity formula at boundary points for a class of nonlinear elliptic partial differential equations, including the obstacle problem case, quenching, a free boundary problem with Bernoulli-type free boundary condition as well as the blow-up case. As application model we prove - for Dirichlet boundary data satisfying certain assumptions - the global existence of a classical solution of the free boundary problem with Bernoulli-type free boundary condition in two and three dimensions. |
| first_indexed | 2024-12-12T21:45:39Z |
| format | Article |
| id | doaj.art-c22291c5a89c45b8a5f64cb9071ea767 |
| institution | Directory Open Access Journal |
| issn | 1072-6691 |
| language | English |
| last_indexed | 2024-12-12T21:45:39Z |
| publishDate | 2004-03-01 |
| publisher | Texas State University |
| record_format | Article |
| series | Electronic Journal of Differential Equations |
| spelling | doaj.art-c22291c5a89c45b8a5f64cb9071ea7672022-12-22T00:10:55ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912004-03-01200444112Boundary monotonicity formulae and applications to free boundary problems I: The elliptic caseGeorg S. WeissWe derive a monotonicity formula at boundary points for a class of nonlinear elliptic partial differential equations, including the obstacle problem case, quenching, a free boundary problem with Bernoulli-type free boundary condition as well as the blow-up case. As application model we prove - for Dirichlet boundary data satisfying certain assumptions - the global existence of a classical solution of the free boundary problem with Bernoulli-type free boundary condition in two and three dimensions.http://ejde.math.txstate.edu/Volumes/2004/44/abstr.htmlFree boundaryboundary regularitynon-tangential touchmonotonicity formulaglobal regularityBernoulli-type free boundary condition. |
| spellingShingle | Georg S. Weiss Boundary monotonicity formulae and applications to free boundary problems I: The elliptic case Electronic Journal of Differential Equations Free boundary boundary regularity non-tangential touch monotonicity formula global regularity Bernoulli-type free boundary condition. |
| title | Boundary monotonicity formulae and applications to free boundary problems I: The elliptic case |
| title_full | Boundary monotonicity formulae and applications to free boundary problems I: The elliptic case |
| title_fullStr | Boundary monotonicity formulae and applications to free boundary problems I: The elliptic case |
| title_full_unstemmed | Boundary monotonicity formulae and applications to free boundary problems I: The elliptic case |
| title_short | Boundary monotonicity formulae and applications to free boundary problems I: The elliptic case |
| title_sort | boundary monotonicity formulae and applications to free boundary problems i the elliptic case |
| topic | Free boundary boundary regularity non-tangential touch monotonicity formula global regularity Bernoulli-type free boundary condition. |
| url | http://ejde.math.txstate.edu/Volumes/2004/44/abstr.html |
| work_keys_str_mv | AT georgsweiss boundarymonotonicityformulaeandapplicationstofreeboundaryproblemsitheellipticcase |