We consider functions that satisfy the identity
for a bounded domain in . Here and , and are suitable nonnegative coefficients such that . In particular, we show that these functions are uniquely determined by their boundary values, approximate -harmonic functions for (for a choice of that depends on and ), and satisfy the strong comparison principle. We also analyze their relation to the theory of tug-of-war games with noise.
@article{ASNSP_2012_5_11_2_215_0, author = {Manfredi, Juan J. and Parviainen, Mikko and Rossi, Julio D.}, title = {On the definition and properties of $p$-harmonious functions}, journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze}, pages = {215--241}, publisher = {Scuola Normale Superiore, Pisa}, volume = {Ser. 5, 11}, number = {2}, year = {2012}, mrnumber = {3011990}, zbl = {1252.91014}, language = {en}, url = {http://archive.numdam.org/item/ASNSP_2012_5_11_2_215_0/} }
TY - JOUR AU - Manfredi, Juan J. AU - Parviainen, Mikko AU - Rossi, Julio D. TI - On the definition and properties of $p$-harmonious functions JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze PY - 2012 SP - 215 EP - 241 VL - 11 IS - 2 PB - Scuola Normale Superiore, Pisa UR - http://archive.numdam.org/item/ASNSP_2012_5_11_2_215_0/ LA - en ID - ASNSP_2012_5_11_2_215_0 ER -
%0 Journal Article %A Manfredi, Juan J. %A Parviainen, Mikko %A Rossi, Julio D. %T On the definition and properties of $p$-harmonious functions %J Annali della Scuola Normale Superiore di Pisa - Classe di Scienze %D 2012 %P 215-241 %V 11 %N 2 %I Scuola Normale Superiore, Pisa %U http://archive.numdam.org/item/ASNSP_2012_5_11_2_215_0/ %G en %F ASNSP_2012_5_11_2_215_0
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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