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An Elliptic PDE with Convex Solutions

Part of: Elliptic equations and systems

Published online by Cambridge University Press:  24 January 2018

Jon Warren
Jon Warren*
Affiliation:
Department of Statistics, University of Warwick, Coventry CV4 7AL, UK ([email protected])
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Abstract

Using a mixture of classical and probabilistic techniques, we investigate the convexity of solutions to the elliptic partial differential equation associated with a certain generalized Ornstein–Uhlenbeck process.

Keywords

convexityelliptic partial differential equationBrownian motion

MSC classification

Primary: 35J25: Boundary value problems for second-order elliptic equations
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 61 , Issue 1 , February 2018 , pp. 201 - 214
Copyright
Copyright © Edinburgh Mathematical Society 2018 

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