On the solvability of the characteristic Dirichlet problem for linear degenerate parabolic equations
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- by Nicolai Kutev, Alessandro Oliaro and Petar Popivanov PDF
- Proc. Amer. Math. Soc. 138 (2010), 153-163 Request permission
Abstract:
We investigate the classical solvability for some classes of linear, degenerate equations in divergence form with prescribed Dirichlet data. Since the boundary value problem is characteristic according to Fichera on a part of the boundary, some typical nonlinear phenomena at these points are observed as boundary gradient blowups of the classical solutions in space directions. The regularity results explain the lack of hypoellipticity for special right-hand sides or boundary data for linear degenerate parabolic equations.References
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Additional Information
- Nicolai Kutev
- Affiliation: Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Acad. G. Bontchev Street, bl. 8, 1113 Sofia, Bulgaria
- Alessandro Oliaro
- Affiliation: Department of Mathematics, University of Torino, Via Carlo Alberto, 10, I-10123 Torino (TO), Italy
- Email: alessandro.oliaro@unito.it
- Petar Popivanov
- Affiliation: Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Acad. G. Bontchev Street, bl. 8, 1113 Sofia, Bulgaria
- Email: popivano@math.bas.bg
- Received by editor(s): September 17, 2008
- Published electronically: August 12, 2009
- Communicated by: Matthew J. Gursky
- © Copyright 2009
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 138 (2010), 153-163
- MSC (2000): Primary 35K65, 35K20, 35B45
- DOI: https://doi.org/10.1090/S0002-9939-09-10053-9
- MathSciNet review: 2550180