Differential and Integral Equations

Subharmonicity, comparison results, and temperature gaps in cylindrical domains

Jeffrey J. Langford

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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

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

First available in Project Euclid: 9 March 2016

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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


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.

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