## Normal derivative for bounded domains with general boundary

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- by Guang Lu Gong, Min Ping Qian and Martin L. Silverstein PDF
- Trans. Amer. Math. Soc.
**308**(1988), 785-809 Request permission

## Abstract:

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.## References

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## Additional Information

- © Copyright 1988 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**308**(1988), 785-809 - MSC: Primary 60J65; Secondary 35A99, 35R60
- DOI: https://doi.org/10.1090/S0002-9947-1988-0951628-0
- MathSciNet review: 951628