Generalized Wentzell boundary conditions for second order operators  with interior degeneracy

Genni  Fragnelli; Gisèle Ruiz Goldstein; Jerome  Goldstein; Rosa Maria  Mininni; Silvia Romanelli

doi:10.3934/dcdss.2016023

Article Contents

2016, Volume 9, Issue 3: 697-715. Doi: 10.3934/dcdss.2016023

This issue Previous Article Identification problem for a degenerate evolution equation with overdetermination on the solution semigroup kernel Next Article Classical solutions to quasilinear parabolic problems with dynamic boundary conditions

Generalized Wentzell boundary conditions for second order operators with interior degeneracy

1.
Department of Mathematics, University of Bari Aldo Moro, Via E.Orabona 4, 70125 Bari
2.
The University of Memphis, Mathematical Sciences, 373 Dunn Hall, Memphis, TN 38152-3240
3.
Department of Mathematical Sciences, University of Memphis, 373 Dunn Hall, Memphis, TN 38152-3240
4.
Dipartimento di Matematica, Università degli Studi di Bari Aldo Moro, via E. Orabona 4, 70125 Bari

Received: April 2015

Revised: September 2015

Published: June 2016

Abstract / Introduction Related Papers Cited by

Abstract

We consider operators in divergence form, $A_1u=(au')'$, and in nondivergence form, $A_2u=au''$, provided that the coefficient $a$ vanishes in an interior point of the space domain. Characterizing the domain of the operators, we prove that, under suitable assumptions, the operators $A_1$ and $A_2$, equipped with general Wentzell boundary conditions, are nonpositive and selfadjoint on spaces of $L^2$ type.

Keywords:

Second order operators in divergence and nondivergence form,
interior degeneracy,
generalized Wentzell boundary conditions.

Mathematics Subject Classification: Primary: 47D06; Secondary: 35K65, 47B25, 47N20.

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References

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