How can I use the hint in the proof? 3. If v is continuous together with its

How can I use the hint in the proof?

Transcribed Image Text:

3. If v is continuous together with its partial derivatives up to the second order, prove that vis subharmonic if and only if Av 0. Hint: For the sufficiency, prove first that v + ex, & > 0, is subharmonic. For the necessity, show that if Av < 0 the mean value over a circle would be a decreasing function of the radius. 3. If v is continuous together with its partial derivatives up to the second order, prove that vis subharmonic if and only if Av 0. Hint: For the sufficiency, prove first that v + ex, & > 0, is subharmonic. For the necessity, show that if Av < 0 the mean value over a circle would be a decreasing function of the radius.

Answer rating: 100% (QA)

The question refers to a property of a realvalued function v that has continuous partial derivatives ... View the full answer