Suppose $u \in C^2(\R^n)$ is a harmonic function. Prove that $v=|\nabla u|^2$ is subharmonic, i.e. $-\Delta v \leq 0$
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.

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
- 1074 views
- $15.00
Related Questions
- Optimization of a multi-objective function
- Let $z = f(x − y)$. Show that $\frac{\partial z}{\partial x}+\frac{\partial z}{\partial y}=0$
- Integral of the fundamentla solution of the heat equation
- Double Integrals, polar coordinates, Stoke's theorem, and Flow line Questions
- Differential Equations
- Partial Derivatives and Graphing Functions
- Parametric, Polar, and Vector-Valued Equations for Kav10
- Uniqueness of solutions of the elliptic equation $\Delta u = u^5 + 2 u^3 + 3 u$