Stability of the mean value formula for harmonic functions in Lebesgue spaces

2020 ◽  
Author(s):  
Giovanni Cupini ◽  
Ermanno Lanconelli
Keyword(s):  
Harmonic Functions ◽  
Mean Value ◽  
Lebesgue Spaces ◽  
The Mean ◽  
Mean Value Formula

scholarly journals Some Remarks on Harmonic Functions in Minkowski Spaces

Mathematics ◽  
2019 ◽  
Vol 7 (2) ◽  
pp. 196
Author(s):  
Songting Yin
Keyword(s):  
Harmonic Function ◽  
Minkowski Space ◽  
Harmonic Functions ◽  
Mean Value ◽  
Mean Value Property ◽  
Minkowski Spaces ◽  
The Mean ◽  
Mean Value Formula

We prove that in Minkowski spaces, a harmonic function does not necessarily satisfy the mean value formula. Conversely, we also show that a function satisfying the mean value formula is not necessarily a harmonic function. Finally, we conclude that in a Minkowski space, if all harmonic functions have the mean value property or any function satisfying the mean value formula must be a harmonic function, then the Minkowski space is Euclidean.

scholarly journals On the mean value property of superharmonic and subharmonic functions

2006 ◽  
Vol 2006 ◽  
pp. 1-3
Author(s):  
Robert Dalmasso
Keyword(s):  
Harmonic Functions ◽  
Mean Value ◽  
Subharmonic Functions ◽  
Mean Value Property ◽  
The Mean

We prove a converse of the mean value property for superharmonic and subharmonic functions. The case of harmonic functions was treated by Epstein and Schiffer.

scholarly journals Almansi Theorem and Mean Value Formula for Quaternionic Slice-regular Functions

2020 ◽  
Vol 30 (4) ◽  
Author(s):  
Alessandro Perotti
Keyword(s):  
Harmonic Functions ◽  
Mean Value ◽  
Zonal Harmonic ◽  
Slice Regular Functions ◽  
Regular Functions ◽  
Quaternionic Polynomials ◽  
Mean Value Formula

Abstract We prove an Almansi Theorem for quaternionic polynomials and extend it to quaternionic slice-regular functions. We associate to every such function f, a pair $$h_1$$ h 1 , $$h_2$$ h 2 of zonal harmonic functions such that $$f=h_1-\bar{x} h_2$$ f = h 1 - x ¯ h 2 . We apply this result to get mean value formulas and Poisson formulas for slice-regular quaternionic functions.

scholarly journals On the mean value property of fractional harmonic functions

2020 ◽  
Vol 201 ◽  
pp. 112112
Author(s):  
Claudia Bucur ◽  
Serena Dipierro ◽  
Enrico Valdinoci
Keyword(s):  
Harmonic Functions ◽  
Mean Value ◽  
Mean Value Property ◽  
The Mean

On the mean-value property of harmonic functions

1965 ◽  
Vol 14 (1) ◽  
pp. 109-111 ◽  
Author(s):  
Bernard Epstein ◽  
M. M. Schiffer
Keyword(s):  
Harmonic Functions ◽  
Mean Value ◽  
Mean Value Property ◽  
The Mean
Sign in / Sign up

Export Citation Format

Share Document