Prove that $\lim_{\epsilon \rightarrow 0} \int_{\partial B(x,\epsilon)} \frac{\partial \Phi}{\partial \nu}(y)f(x-y)dy=f(x)$
I'd like to show that
$$\lim_{\epsilon \rightarrow 0} \int_{\partial B(x,\epsilon)} \frac{\partial \Phi}{\partial \nu}(y)f(x-y)dy=f(x)$$
where $\phi$ is the fundamental solution of the laplacian in dimesnion $n\geq 3$ and $f$ is a continuous function.
Mathlearner
28
Answer
Answers can only be viewed under the following conditions:
- The questioner was satisfied with and accepted the answer, or
- The answer was evaluated as being 100% correct by the judge.
Erdos
4.8K
The answer is accepted.
Join Matchmaticians Affiliate Marketing
Program to earn up to a 50% commission on every question that your affiliated users ask or answer.
- answered
- 640 views
- $7.00
Related Questions
- Differential equations
- [ Banach Fixt Point Theorem ] $\frac{dy} {dx} = xy, \text{with} \ \ y(0) = 3,$
- Find $\lim_{x\rightarrow \infty} \frac{1}{x^2}\sin x^2\tan x$
- Limits : $x^{-1} \sin(x) $ as x -> 0 and $\tfrac{\ln(x)}{1-x}$ as x-> 0
- Proof of P = Fv.
- Partial differential equations help
- Compute $\lim _{n \rightarrow \infty} \frac{1}{n}\ln \frac{(2n)!}{n^n n!}$
- Week solution of the equation $u_t + u^2u_x = f(x,t)$