One-dimensional symmetry for semilinear equations with unbounded drift

Annalisa Cesaroni; Matteo Novaga; Andrea Pinamonti

doi:10.3934/cpaa.2013.12.2203

Article Contents

2013, Volume 12, Issue 5: 2203-2211. Doi: 10.3934/cpaa.2013.12.2203

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One-dimensional symmetry for semilinear equations with unbounded drift

1.
Dip. di Matematica Pura e Applicata, Univ. di Padova, via Trieste 63, 35131 Padova
2.
Università di Padova, Via Trieste 63, 35121 Padova
3.
Dipartimento di Matematica, Università di Padova, Via Trieste 63, Padova

Received: June 2012

Revised: October 2012

Published: September 2013

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Abstract

We consider semilinear equations with unbounded drift in the whole of $R^n$ and we show that monotone solutions with finite energy are one-dimensional.

Keywords:

Symmetry and monotonicity properties of solutions,
semilinear elliptic PDEs,
energy estimates,
Ornstein-Uhlenbeck type operators,
Liouville theorems,
Poincaré-type inequality.

Mathematics Subject Classification: Primary: 35J61; Secondary: 35J20, 35B06.

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