AN ASYMPTOTIC MEAN VALUE CHARACTERIZATION FOR p-HARMONIC FUNCTIONS

作者：Manfredi Juan J^*; Parviainen Mikko; Rossi Julio D

来源：Proceedings of the American Mathematical Society, 2010, 138(3): 881-889.

DOI：10.1090/S0002-9939-09-10183-1

• p-Laplacian
• infinity Laplacian
• mean value property
• viscosity solutions

characterize p-harmonic functions in tern-is of an asymptotic mean value property. A p-harmonic function u is a viscosity solution to Delta(p)u = div(vertical bar del(u)vertical bar(p-2) with = 0 < p <= infinity in a domain Omega if and only if the expansion
u(x) = alpha/2{max u/B(epsilon)(x) + min u/B(epsilon)(x)} + beta/vertical bar B(epsilon)(x)vertical bar integral(B epsilon(x)) udy + o(epsilon(2))
holds as epsilon -> 0 for x is an element of Omega in a Weak sense, which we call the viscosity sense. Here the coefficients alpha, beta are determined by alpha + beta = 1 and alpha/beta = (p - 2)/(N + 2).

• 出版日期2010-3