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On the solvability of the characteristic Dirichlet problem for linear degenerate parabolic equations


Authors: Nicolai Kutev, Alessandro Oliaro and Petar Popivanov
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
Published electronically: August 12, 2009
MathSciNet review: 2550180
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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.


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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

DOI: https://doi.org/10.1090/S0002-9939-09-10053-9
Keywords: Degenerate parabolic equations, characteristic Dirichlet problem, hypoellipticity, elliptic regularization, a priori estimates.
Received by editor(s): September 17, 2008
Published electronically: August 12, 2009
Communicated by: Matthew J. Gursky
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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