Differential and Integral Equations

Comparison results for linear parabolic equations in unbounded domains via Gaussian symmetrization

F. Chiacchio

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Abstract

We study the effect on the solutions of linear parabolic equations of Gaussian symmetrization. This kind of symmetrization, which transforms a domain into an half-space with the same Gaussian measure, is specifically useful when the domain is unbounded. The main tools we use are the properties of the weighted rearrangements and in particular the isoperimetric inequality with respect to Gaussian measure.

Article information

Source
Differential Integral Equations Volume 17, Number 3-4 (2004), 241-258.

Dates
First available in Project Euclid: 21 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.die/1356060433

Mathematical Reviews number (MathSciNet)
MR2037978

Zentralblatt MATH identifier
1174.35305

Subjects
Primary: 35B05: Oscillation, zeros of solutions, mean value theorems, etc.
Secondary: 35K20: Initial-boundary value problems for second-order parabolic equations

Citation

Chiacchio, F. Comparison results for linear parabolic equations in unbounded domains via Gaussian symmetrization. Differential Integral Equations 17 (2004), no. 3-4, 241--258. https://projecteuclid.org/euclid.die/1356060433.


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