| Citation: |
Zifei Shen, Shuijin Zhang. SOLVABILITY OF QUASILINEAR MAXWELL EQUATIONS IN EXTERIOR DOMAINS[J]. Journal of Applied Analysis & Computation, 2023, 13(6): 3477-3490. doi: 10.11948/20230121
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SOLVABILITY OF QUASILINEAR MAXWELL EQUATIONS IN EXTERIOR DOMAINS
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Abstract
In this paper we consider some q-curl-curl equations with lack of compactness. Our analysis is developed in the abstract setting of exterior domains. We first recall a decomposition of $ {\rm curl} $-free space based on $ L^{r} $-Helmholtz-Weyl decomposition in exterior domains. Then by reducing the original system into a div-curl system and a $ p $-Laplacian equation with Neumann boundary condition, we obtain the solvability of solutions for the q-curl-curl equation.
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Keywords:
- Helmholtz-Weyl decomposition /
- solvability /
- Maxwell equation /
- exterior domains
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References
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Zifei Shen, Shuijin Zhang. SOLVABILITY OF QUASILINEAR MAXWELL EQUATIONS IN EXTERIOR DOMAINS[J]. Journal of Applied Analysis & Computation, 2023, 13(6): 3477-3490. doi: 10.11948/20230121
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