Bodies for which harmonic functions satisfy the mean value property
نویسندگان
چکیده
منابع مشابه
BODIES FOR WHICH HARMONIC FUNCTIONS SATISFY THE MEAN VALUE PROPERTY(x)
where „((?)= const depending on n. In this paper we consider the converse problem, namely: Suppose (0.1) holds for all harmonic functions, is S necessarily a sphere with center P (and consequently „^const)? The answer is in general negative, unless some assumptions are made on „. Thus, (0.1) is always satisfied with „(Q) = —dG(P, Q)/dv, G being Green's function of the Laplace equation in D and ...
متن کاملInvariant Mean Value Property and Harmonic Functions
We give conditions on the functions σ and u on R such that if u is given by the convolution of σ and u, then u is harmonic on R.
متن کاملHarmonic functions via restricted mean-value theorems
Let f be a function on a bounded domain Ω ⊆ R and δ be a positive function on Ω such that B(x, δ(x)) ⊆ Ω. Let σ(f)(x) be the average of f over the ball B(x, δ(x)). The restricted mean-value theorems discuss the conditions on f, δ, and Ω under which σ(f) = f implies that f is harmonic. In this paper, we study the stability of harmonic functions with respect to the map σ. One expects that, in gen...
متن کاملA Mean Value Property of Harmonic Functions on the Interior of a Hyperbola
We establish a mean value property for harmonic functions on the interior of a hyperbola. This property connects their boundary values with the interior ones on the axis of the hyperbola from the focus to infinity.
متن کاملA Mean Value Property of Harmonic Functions on Prolate Ellipsoids of Revolution
We establish a mean value property for harmonic functions on the interior of a prolate ellipsoid of revolution. This property connects their boundary values with those on the interfocal segment.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 1962
ISSN: 0002-9947
DOI: 10.1090/s0002-9947-1962-0151627-7