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Media type:
E-Article
Title:
Normal Derivative for Bounded Domains with General Boundary
Contributor:
Guanglu, Gong;
Minping, Qian;
Silverstein, Martin L.
imprint:
American Mathematical Society, 1988
Published in:Transactions of the American Mathematical Society
Language:
English
ISSN:
0002-9947
Origination:
Footnote:
Description:
<p>Let $D$ be a general bounded domain in the Euclidean space $R^n$. A Brownian motion which enters from and returns to the boundary symmetrically is used to define the normal derivative as a functional for $f$ with $f$, $\nabla f$ and $\Delta f$ all in $L^2$ on $D$. The corresponding Neumann condition (normal derivative $= 0$) is an honest boundary condition for the $L^2$ generator of reflected Brownian notion on $D$. A conditioning argument shows that for $D$ and $f$ sufficiently smooth this general definition of the normal derivative agrees with the usual one.</p>