A priori Holder and Lipschitz regularity for generalized p-harmonious functions in metric measure spaces

作者：Arroyo Angel; Llorente Jose G^*

来源：Nonlinear Analysis-Theory Methods & Applications, 2018, 168: 32-49.

DOI：10.1016/j.na.2017.11.007

• Mean value property
• p-harmonious
• p-laplacian
• Metric measure spaces

Let (X, d, mu) be a proper metric measure space and let Omega subset of X be a bounded domain. For each x is an element of Omega, we choose a radius 0 < rho(x) <= dist(x, partial derivative Omega) and let B-x be the closed ball centered at x with radius rho(x). If alpha is an element of R, consider the following operator in C(<(Omega)over bar>),
T(alpha)u(x) = alpha/2 (sup(Bx) u + inf(Bx) u) + 1-alpha/mu(B-x) integral(u)(Bx) (d mu).
Under appropriate assumptions on alpha, X, mu and the radius function. we show that solutions u is an element of C((Omega) over bar) of the functional equation T(alpha)u = u satisfy a local Holder or Lipschitz condition in Omega. The motivation comes from the so called p-harmonious functions in euclidean domains.

• 出版日期2018-3