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3. The Helmholtz decomposition of vector fields for two-dimensional exterior Lipschitz domains.

Author

Watanabe, Keiichi

Subjects
VECTOR fields, HELMHOLTZ equation
Abstract

Let Ω be an exterior Lipschitz domain in R². It is proved that the Helmholtz decomposition of the vector fields in Lp(Ω; R²) exists if p satisfies |1/p−1/2| < 1/4+ε with some constant ε = ε(Ω) ∈ (0, 1/4], where it is allowed to take ε = 1/4 if ∂Ω ∈ C¹. [ABSTRACT FROM AUTHOR]

Published
2024
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