Geodesic
PDE comparison principles for Robin problems
Canadian journal of mathematics, Tome 75 (2023) no. 1, pp. 108-139

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DOI

We compare the solutions of two Poisson problems in a spherical shell with Robin boundary conditions, one with given data, and one where the data have been cap symmetrized. When the Robin parameters are nonnegative, we show that the solution to the symmetrized problem has larger convex means. Sending one of the Robin parameters to $+\infty $, we obtain mixed Robin/Dirichlet comparison results in shells. We prove similar results on balls and prove a comparison principle on generalized cylinders with mixed Robin/Neumann boundary conditions.
DOI : 10.4153/S0008414X21000547
Mots-clés : Symmetrization, comparison theorems, Poisson’s equation, Robin boundary conditions 
Langford, Jeffrey J. PDE comparison principles for Robin problems. Canadian journal of mathematics, Tome 75 (2023) no. 1, pp. 108-139. doi: 10.4153/S0008414X21000547
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     title = {PDE comparison principles for {Robin} problems},
     journal = {Canadian journal of mathematics},
     pages = {108--139},
     year = {2023},
     volume = {75},
     number = {1},
     doi = {10.4153/S0008414X21000547},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/S0008414X21000547/}
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