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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Dirichlet boundary conditions for elliptic operators with unbounded drift
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by A. Lunardi, G. Metafune and D. Pallara PDF
Proc. Amer. Math. Soc. 133 (2005), 2625-2635 Request permission

Erratum: Proc. Amer. Math. Soc. 134 (2006), 2479-2480.

Abstract:

We study the realisation $A$ of the operator $\mathcal {A} = \Delta - \langle D\Phi , D\cdot \rangle$ in $L^2(\Omega , \mu )$ with Dirichlet boundary condition, where $\Omega$ is a possibly unbounded open set in $\mathbb {R}^N$, $\Phi$ is a semi-convex function and the measure $d\mu (x) = \exp (-\Phi (x)) dx$ lets $\mathcal {A}$ be formally self-adjoint. The main result is that $A:D(A)= \{u\in H^2(\Omega , \mu ): \langle D\Phi , Du \rangle \in L^2(\Omega , \mu ), u=0$ at $\partial \Omega \}$ is a dissipative self-adjoint operator in $L^2(\Omega , \mu )$.
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Additional Information
  • A. Lunardi
  • Affiliation: Dipartimento di Matematica, Università di Parma, Parco Area delle Scienze 53, 43100 Parma, Italy
  • MR Author ID: 116935
  • Email: lunardi@unipr.it
  • G. Metafune
  • Affiliation: Dipartimento di Matematica “Ennio De Giorgi”, Università di Lecce, C.P.193, 73100, Lecce, Italy
  • MR Author ID: 123880
  • Email: giorgio.metafune@unile.it
  • D. Pallara
  • Affiliation: Dipartimento di Matematica “Ennio De Giorgi”, Università di Lecce, C.P.193, 73100, Lecce, Italy
  • Email: diego.pallara@unile.it
  • Received by editor(s): April 19, 2004
  • Published electronically: April 19, 2005
  • Communicated by: David S. Tartakoff
  • © Copyright 2005 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 133 (2005), 2625-2635
  • MSC (2000): Primary 35J70; Secondary 47D07
  • DOI: https://doi.org/10.1090/S0002-9939-05-08068-8
  • MathSciNet review: 2146208