Differential and Integral Equations

Subharmonicity, comparison results, and temperature gaps in cylindrical domains

Jeffrey J. Langford

Full-text: Access denied (no subscription detected) We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Abstract

In this paper, we compare the solutions of two Poisson PDE's in cylinders with Neumann boundary conditions, one with given initial data and one with data arranged decreasing in the $y-$direction. When the solutions are normalized to have zero mean, we show that the solution with symmetrized data is itself symmetrized and exhibits larger convex means. The main tools used are the $\star-$function introduced by Baernstein and a new subharmonicity result. As a consequence, we give a new proof of a conjecture of Kawohl for temperature gaps in rectangles.

Article information

Source
Differential Integral Equations Volume 29, Number 5/6 (2016), 493-512.

Dates
First available in Project Euclid: 9 March 2016

Permanent link to this document
https://projecteuclid.org/euclid.die/1457536888

Mathematical Reviews number (MathSciNet)
MR3471970

Zentralblatt MATH identifier
06562186

Subjects
Primary: 35J05: Laplacian operator, reduced wave equation (Helmholtz equation), Poisson equation [See also 31Axx, 31Bxx] 35B05: Oscillation, zeros of solutions, mean value theorems, etc.

Citation

Langford, Jeffrey J. Subharmonicity, comparison results, and temperature gaps in cylindrical domains. Differential Integral Equations 29 (2016), no. 5/6, 493--512. https://projecteuclid.org/euclid.die/1457536888.


Export citation