We provide explicit criteria for uniqueness or nonuniqueness of solutions to a wide class of second order elliptic and parabolic problems. The operator coefficients may be unbounded or vanish, or not to have a limit when approaching some part of the boundary, referred to as singular boundary. We discuss whether boundary conditions should be imposed on such a part to ensure well-posedness. The answer depends on the dimension of the singular boundary, and possibly on the behavior of coefficients near it. © 2008 Elsevier Masson SAS. All rights reserved.
Criteria for well-posedness of degenerate elliptic and parabolic problems / Pozio, Maria Assunta; Punzo, Fabio; Tesei, Alberto. - In: JOURNAL DE MATHÉMATIQUES PURES ET APPLIQUÉES. - ISSN 0021-7824. - 90:4(2008), pp. 353-386. [10.1016/j.matpur.2008.06.001]
Criteria for well-posedness of degenerate elliptic and parabolic problems
POZIO, Maria Assunta;PUNZO, FABIO;TESEI, Alberto
2008
Abstract
We provide explicit criteria for uniqueness or nonuniqueness of solutions to a wide class of second order elliptic and parabolic problems. The operator coefficients may be unbounded or vanish, or not to have a limit when approaching some part of the boundary, referred to as singular boundary. We discuss whether boundary conditions should be imposed on such a part to ensure well-posedness. The answer depends on the dimension of the singular boundary, and possibly on the behavior of coefficients near it. © 2008 Elsevier Masson SAS. All rights reserved.| File | Dimensione | Formato | |
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