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.
|Titolo:||Criteria for well-posedness of degenerate elliptic and parabolic problems|
|Parole Chiave:||Singular elliptic and parabolic problems; Upper and lower solutions; Well-posedness|
|Settore Scientifico Disciplinare:||Settore MAT/05 - Analisi Matematica|
|Data di pubblicazione:||2008|
|Digital Object Identifier (DOI):||10.1016/j.matpur.2008.06.001|
|Appare nelle tipologie:||01 - Articolo su periodico|