Second order elliptic operators in $L^2$ with first order degeneration at the boundaryand outward pointing drift

Simona Fornaro; Giorgio Metafune; Diego Pallara; Roland Schnaubelt

doi:10.3934/cpaa.2015.14.407

Article Contents

2015, Volume 14, Issue 2: 407-419. Doi: 10.3934/cpaa.2015.14.407

This issue Previous Article On the asymptotic stability of Volterra functional equations with vanishing delays Next Article On small perturbation of four-dimensional quasi-periodic system with degenerate equilibrium point

Second order elliptic operators in $L^2$ with first order degeneration at the boundary and outward pointing drift

1.
Dipartimento di Matematica "F. Casorati”, Università di Pavia, Via Ferrata 1, 27100 Pavia
2.
Dipartimento di Matematica E. De Giorgi, Università del Salento, 73100, Lecce
3.
Dipartimento di Matematica "Ennio De Giorgi”, Università del Salento, C.P. 193, Lecce, I-73100
4.
Department of Mathematics, Karlsruhe Institute of Technology, 76128 Karlsruhe

Received: December 2013

Revised: July 2014

Published: March 2015

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Abstract

We study second order elliptic operators whose diffusion coefficients degenerate at the boundary in first order and whose drift term strongly points outward. It is shown that these operators generate analytic semigroups in $L^2$ where they are equipped with their natural domain without boundary conditions. Hence, the corresponding parabolic problem can be solved with optimal regularity. In a previous work we had treated the case of inward pointing drift terms.

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Mathematics Subject Classification: Primary: 35K65, 35J70.

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