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
4.7K
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
- 607 views
- $7.00
Related Questions
- Explicit formula for the trasport equation
- Suppose $u \in C^2(\R^n)$ is a harmonic function. Prove that $v=|\nabla u|^2$ is subharmonic, i.e. $-\Delta v \leq 0$
- [ Banach Fixt Point Theorem ] $\frac{dy} {dx} = xy, \text{with} \ \ y(0) = 3,$
- Find a formula for the vector hyperbolic problem
- Compute $\lim _{n \rightarrow \infty} \frac{1}{n}\ln \frac{(2n)!}{n^n n!}$
- Find solutions to the Riemann Problems
- Help with 2 PDE questions
- Studying the graph of this function