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(2000 / vol.3 / no.1)
Methods of Proving Symmetry of Solutions to Elliptic Boundary Value Problems
Jeong-Seon Baek
Pages. 17-23     



This paper is a brief survey on the method of proving symmetry of
solutions to semilinear elliptic problems involving Laplacian,
$p$-Laplacian, poly-Laplacian, $A$-Laplacian and convex-Laplacian
operators. Various results are introduced and a brief illustration
on the most successful method, the moving plane method, is shown.



1. Model Problem 2. Non-radial Example 3. Typical affirmative results 4. $p$-Laplacian Case 5. $A$-Laplacian Case(See [32]) 6. Convex-Laplacian 7. Poly-Laplacian Case (Higher Order Laplacian) 8. Briefing of Methods



semi-linear, radial, symmetric, elliptic, moving plane method, symmetrization, variational, Laplacian, $p$-Laplacian, $A$-Laplacian, convex-Laplacian, poly-Laplacian



35J25, 35J30, 35J60, 35J65, 35