Existence of non-radially symmetric viscosity solutions to semilinear degenerate elliptic equations with radially symmetric coefficients in the plane, Part I |
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| Authors: | Kenji Maruo |
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| Institution: | a Department of Maritime Transportation Systems, Faculty of Maritime Sciences, Kobe University, Japan
b Department of Applied Mathematics, Faculty of Science, Fukuoka University, Japan |
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| Abstract: | We prove the existence of non-radially symmetric solutions for semilinear degenerate elliptic equations with radially symmetric coefficients in the plane. We adapt the viscosity solution for the weak solution. The key arguments consist of the analysis of the structure of 2π-periodic solutions for the associated Laplace-Beltrami operator and construction of super- and sub-solutions which have the prescribed asymptotic structures. |
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| Keywords: | Non-radially symmetric solution Degenerate elliptic equation Semilinear elliptic equation Viscosity solution |
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