An asymptotic mean value characterization for $p$-harmonic functions
نویسندگان
چکیده
منابع مشابه
Invariant 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 کاملCHARACTERIZATION BY ASYMPTOTIC MEAN FORMULAS OF q−HARMONIC FUNCTIONS IN CARNOT GROUPS
Aim of this paper is to extend the work [9] to the Carnot group setting. More precisely, we prove that in every Carnot group a function is q−harmonic (here 1 < q < ∞), if and only if it satisfies a particular asymptotic mean value formula.
متن کاملAsymptotic Behavior of Infinity Harmonic Functions Near an Isolated Singularity
In this paper, we prove that if n ≥ 2 and x0 is an isolated singularity of a non-negative infinity harmonic function u, then either x0 is a removable singularity of u or u(x) = u(x0) + c|x − x0| + o(|x − x0|) near x0 for some fixed constant c = 0. In particular, if x0 is nonremovable, then u has a local maximum or a local minimum at x0. We also prove a Bernstein-type theorem, which asserts that...
متن کاملBODIES 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 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: Proceedings of the American Mathematical Society
سال: 2010
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-09-10183-1