# Pointwise estimate for solutions of the laplace equation on bounded domains

$$\max |u| \leq C (\max_{\partial \Omega }|g|+\max_{\overline{\Omega} }|f|), $$

where $u$ is a solutions of the PDE

$$ -\Delta u=f $$ with $u=g$ on $\partial \Omega$.

## Answer

**Answers can be viewed only if**

- The questioner was satisfied and accepted the answer, or
- The answer was disputed, but the judge evaluated it as 100% correct.

The answer is accepted.

Join Matchmaticians Affiliate Marketing
Program to earn up to 50% commission on every question your affiliated users ask or answer.

- answered
- 182 views
- $25.00

### Related Questions

- Integral of the fundamentla solution of the heat equation
- Find solutions to the Riemann Problems
- Uniqueness of solutions of the elliptic equation $\Delta u = u^5 + 2 u^3 + 3 u$
- Optimisation Problem
- Why does this spatial discretization with n intervals have a position of (n-1)/n for each interval?
- Maxwell's equations and the wave equation
- Can someone translate $s_j : \Omega \hspace{3pt} x \hspace{3pt} [0,T_{Final}] \rightarrow S_j \subset R$ into simple English for me?
- Week solution of the equation $u_t + u^2u_x = f(x,t)$