The Robin problem for the scalar Oseen equation

Medková, Dagmar; Skopin, Emma; Varnhorn, Werner

doi:10.1002/mma.2749

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Potentials For the Scalar Oseen Equation1

Introduction1

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2017

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“…Clearly

E_{λ} false(- x false) = E_{- λ} false(x false)

. We have

false| E_{λ} false(x false) - E_{0} (x) false| = O (1), false| \nabla E_{λ} false(x false) - \nabla E_{0} (x) false| = O ({false| x false|}^{- 1}) as false| x false| \to 0

by [, Lemma 3.2]. If

α = (α_{1}, α_{2}, α_{3})

is a multiindex and

λ \neq 0

then

|\partial^{α} E_{0}^{Ω} φ (x)| = O ({false| x false|}^{- 1 - false| α false|}) as false| x false| \to \infty,

|\partial^{α} E_{λ}^{Ω} φ (x)| = O (e^{- false(false| λ x false| - λ x_{1} false) / 2} {false| x false|}^{- 1}) as false| x false| \to \infty,

where

false| α false| = α_{1} + α_{2} + α_{3 <...>}

…”

Section: Potentials For the Scalar Oseen Equationunclassified

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‐solution of the Neumann, Robin and transmission problem for the scalar Oseen equation

Medková

2017

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“…Clearly

E_{λ} false(- x false) = E_{- λ} false(x false)

. We have

false| E_{λ} false(x false) - E_{0} (x) false| = O (1), false| \nabla E_{λ} false(x false) - \nabla E_{0} (x) false| = O ({false| x false|}^{- 1}) as false| x false| \to 0

by [, Lemma 3.2]. If

α = (α_{1}, α_{2}, α_{3})

is a multiindex and

λ \neq 0

then

|\partial^{α} E_{0}^{Ω} φ (x)| = O ({false| x false|}^{- 1 - false| α false|}) as false| x false| \to \infty,

|\partial^{α} E_{λ}^{Ω} φ (x)| = O (e^{- false(false| λ x false| - λ x_{1} false) / 2} {false| x false|}^{- 1}) as false| x false| \to \infty,

where

false| α false| = α_{1} + α_{2} + α_{3 <...>}

…”

Section: Potentials For the Scalar Oseen Equationunclassified

“…All these results concern the exterior Dirichlet problem. Lately classical solutions of the Dirichlet problem, the Neumann problem and the Robin problem for the scalar Oseen equation has been studied by the integral equation method ().…”

Section: Introductionmentioning

confidence: 99%

‐solution of the Neumann, Robin and transmission problem for the scalar Oseen equation

Medková

2017

Mathematische Nachrichten

Self Cite

View full text Add to dashboard Cite

show abstract

The Robin problem for the scalar Oseen equation

Cited by 1 publication

References 15 publications

‐solution of the Neumann, Robin and transmission problem for the scalar Oseen equation

‐solution of the Neumann, Robin and transmission problem for the scalar Oseen equation

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