5. Let CR" be a domain and let u € C²(2). Show that u if u is subharmonic then Au 20 in 2. Hint: Assume Au(20) <0 for some ro. Then Au(ro) <0 in B(ro, r) for some r >0. Use 4. to deduce that -u is subharmonic in B(ro, r) which implies that u satisfies the mean value property in B(ro, r). Then conclude a contradiction.
5. Let CR" be a domain and let u € C²(2). Show that u if u is subharmonic then Au 20 in 2. Hint: Assume Au(20) <0 for some ro. Then Au(ro) <0 in B(ro, r) for some r >0. Use 4. to deduce that -u is subharmonic in B(ro, r) which implies that u satisfies the mean value property in B(ro, r). Then conclude a contradiction.
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Transcribed Image Text:5. Let CR" be a domain and let u € C²(2). Show that u if u is subharmonic then
Au 20 in 2.
Hint: Assume Au(20) <0 for some ro. Then Au(ro) <0 in B(ro, r) for some r >0. Use 4.
to deduce that -u is subharmonic in B(ro, r) which implies that u satisfies the mean value
property in B(ro, r). Then conclude a contradiction.
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