On the definition and properties of p-harmonious functions
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 5, Volume 11 (2012) no. 2, pp. 215-241.

We consider functions that satisfy the identity

u ϵ (x)=α 2sup B ¯ ϵ (x) u ϵ +inf B ¯ ϵ (x) u ϵ +β- B ϵ (x) u ϵ dy

for a bounded domain in n . Here ϵ>0 and α, and β are suitable nonnegative coefficients such that α+β=1. In particular, we show that these functions are uniquely determined by their boundary values, approximate p-harmonic functions for 2p< (for a choice of p that depends on α and β), and satisfy the strong comparison principle. We also analyze their relation to the theory of tug-of-war games with noise.

Published online:
Classification: 91A15, 35B50, 35J25, 35J70, 49N70, 91A24
Manfredi, Juan J. 1; Parviainen, Mikko 2; Rossi, Julio D. 3

1 Department of Mathematics, University of Pittsburgh Pittsburgh, PA 15260, USA
2 Department of Mathematics and Statistics P.O. Box 35 FI-40014 University of Jyväskylä Finland
3 Departamento de Análisis Matemático Universidad de Alicante Ap. correos 99, 03080, Alicante, Spain On leave from: Departamento de Matemática FCEyN UBA 14128, Buenos Aires, Argentina
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Manfredi, Juan J.; Parviainen, Mikko; Rossi, Julio D. On the definition and properties of $p$-harmonious functions. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 5, Volume 11 (2012) no. 2, pp. 215-241. http://archive.numdam.org/item/ASNSP_2012_5_11_2_215_0/

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