Artículo

Del Pezzo, L.M.; Mosquera, C.A.; Rossi, J.D. "Estimates for nonlinear harmonic measures on trees" (2014) Bulletin of the Brazilian Mathematical Society. 45(3):405-432
Estamos trabajando para incorporar este artículo al repositorio
Consulte el artículo en la página del editor
Consulte la política de Acceso Abierto del editor

Abstract:

In this paper we give some estimates for nonlinear harmonic measures on trees. In particular, we estimate in terms of the size of a set D the value at the origin of the solution to u(x) = F((x, 0),..,(x,m − 1)) for every x ∈ (Equation Present), a directed tree with m branches with initial datum f + χD. Here F is an averaging operator on ℝm, x is a vertex of a directed tree (Equation Present) with regular m-branching and (x, i) denotes a successor of that vertex for 0 ≤ i ≤ m − 1. © 2014, Sociedade Brasileira de Matemática.

Registro:

Documento: Artículo
Título:Estimates for nonlinear harmonic measures on trees
Autor:Del Pezzo, L.M.; Mosquera, C.A.; Rossi, J.D.
Filiación:CONICET and Departamento de Matemática, FCEyN, Universidad de Buenos Aires, Pabellon I, Ciudad Universitaria (1428), Buenos Aires, Argentina
Departamento de Análisis Matemático, Universidad de Alicante, Ap. correo 99, Alicante, 03080, Spain
Palabras clave:averaging operators; directed trees; harmonic measures
Año:2014
Volumen:45
Número:3
Página de inicio:405
Página de fin:432
DOI: http://dx.doi.org/10.1007/s00574-014-0056-8
Título revista:Bulletin of the Brazilian Mathematical Society
Título revista abreviado:Bull. Braz. Math. Soc.
ISSN:16787544
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_16787544_v45_n3_p405_DelPezzo

Referencias:

  • Alvarez, V., Rodríguez, J.M., Yakubovich, D.V., Estimates for nonlinear harmonic “measures” on trees (2001) Michigan Math. J., 49 (1), pp. 47-64
  • Aviles, P., Manfredi, J.J., On null sets of P-harmonic measures (1992) Partial differential equations with minimal smoothness and applications (Chicago, IL, 1990), 42, pp. 33-36
  • Björn, A., Björn, J., Shanmugalingam, N., A problem of Baernstein on the equality of the p-harmonic measure of a set and its closure (2006) Proc. Amer. Math. Soc., 134 (2), pp. 509-519
  • Del Pezzo, L.M., Mosquera, C.A., Rossi, J.D., The unique continuation property for a nonlinear equation on trees (2014) Journal of the London Mathematical Society, 89 (2), pp. 364-382
  • Granlund, S., Lindqvist, P., Martio, O., F-harmonic measure in space (1982) Ann. Acad. Sci. Fenn. Ser. A I Math., 7 (2), pp. 233-247
  • Heinonen, J., Kilpeläinen, T., Martio, O., Nonlinear potential theory of degenerate elliptic equations (1993) Oxford Mathematical Monographs. Oxford Science Publications, , The Clarendon Press, Oxford University Press, New York:
  • Hartenstine, D., Rudd, M., Asymptotic statistical characterizations of pharmonic functions of two variables (2011) Rocky Mountain J. Math., 41 (2), pp. 493-504
  • Hartenstine, D., Rudd, M., Statistical functional equations and p-harmonious functions (2013) Adv. Nonlinear Stud., 13 (1), pp. 191-207
  • Kaufman, R., Llorente, J.G., Wu, J.-M., Nonlinear harmonic measures on trees (2003) Ann. Acad. Sci. Fenn. Math., 28 (2), pp. 279-302
  • Kaufman, R., Wu, J.-M., Fatou theorem of p-harmonic functions on trees (2000) Ann. Probab., 28 (3), pp. 1138-1148
  • Kurki, J., Invariant sets for [Math Processing Error]-harmonic measure (1995) Ann. Acad. Sci. Fenn. Ser. A I Math., 20 (2), pp. 433-436
  • Llorente, J.G., Manfredi, J.J., Wu, J.M., p-harmonic measure is not additive on null sets (2005) Ann. Sc. Norm. Super. Pisa Cl. Sci., 4 (2), pp. 357-373
  • Manfredi, J.J., Parviainen, M., Rossi, J.D., On the definition and properties of p-harmonious functions (2012) Annali della Scuola Normale Superiore di Pisa, Clase di Scienze, XI (2), pp. 215-241
  • Manfredi, J.J., Parviainen, M., Rossi, J.D., An asymptotic mean value characterization for p-harmonic functions (2010) Procc. American Mathematical Society., 138, pp. 881-889
  • J.J. Manfredi, A. Oberman and A. Sviridov. Nonlinear elliptic PDEs on graphs. Preprint; Mathematisches Institut (1989) Jyväskylä, p. 23
  • Peres, Y., Schramm, O., Sheffield, S., Wilson, D., Tug-of-war and the infinity Laplacian (2011) Selected works of Oded Schramm, 1, pp. 595-638
  • Peres, Y., Sheffield, S., Tug-of-war with noise: a game theoretic view of the p-Laplacian (2008) Duke Math. J., 145 (1), pp. 91-120
  • Oberman, A., Finite Difference Methods for the infinity Laplace and p-Laplace equations (2013) J. Comput. Appl. Math., 254, pp. 65-80
  • Oberman, A., A convergent difference scheme for the infinity Laplacian: construction of absolutely minimizing Lipschitz extensions (2005) Math. Comp., 74, pp. 1217-1230
  • Rudd, M., Van Dyke, H.A., Median values, 1-harmonic functions, and functions of least gradient (2013) Commun. Pure Appl. Anal., 12 (2), pp. 711-719
  • Sviridov, A.P., (2011) Elliptic equations in graphs via stochastic games
  • Sviridov, A.P., p-harmonious functions with drift on graphs via games (2011) Electron. J. Differential Equations, 114, p. 11
  • Wolff, T.H., Gap series constructions for the p-Laplacian (2007) Paper completed by John Garnett and Jang-Mei Wu. J. Anal. Math., 102, pp. 371-394

Citas:

---------- APA ----------
Del Pezzo, L.M., Mosquera, C.A. & Rossi, J.D. (2014) . Estimates for nonlinear harmonic measures on trees. Bulletin of the Brazilian Mathematical Society, 45(3), 405-432.
http://dx.doi.org/10.1007/s00574-014-0056-8
---------- CHICAGO ----------
Del Pezzo, L.M., Mosquera, C.A., Rossi, J.D. "Estimates for nonlinear harmonic measures on trees" . Bulletin of the Brazilian Mathematical Society 45, no. 3 (2014) : 405-432.
http://dx.doi.org/10.1007/s00574-014-0056-8
---------- MLA ----------
Del Pezzo, L.M., Mosquera, C.A., Rossi, J.D. "Estimates for nonlinear harmonic measures on trees" . Bulletin of the Brazilian Mathematical Society, vol. 45, no. 3, 2014, pp. 405-432.
http://dx.doi.org/10.1007/s00574-014-0056-8
---------- VANCOUVER ----------
Del Pezzo, L.M., Mosquera, C.A., Rossi, J.D. Estimates for nonlinear harmonic measures on trees. Bull. Braz. Math. Soc. 2014;45(3):405-432.
http://dx.doi.org/10.1007/s00574-014-0056-8