Artículo

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 study the game -Laplacian on a tree, that is, here is a vertex of the tree and is the set of successors of. We study the family of the subsets of the tree that enjoy the unique continuation property, that is, subsets such that implies. © 2014 © 2014 London Mathematical Society.

Registro:

Documento: Artículo
Título:The unique continuation property for a nonlinear equation on trees
Autor:Del Pezzo, L.M.; Mosquera, C.A.; Rossi, J.D.
Filiación:CONICET and Departamento de Matemática, FCEyN, Ciudad Universitaria, 1428 Buenos Aires, Argentina
Departamento de Análisis Matemático, Universidad de Alicante, Ap. correo 99, 03080 Alicante, Spain
Año:2014
Volumen:89
Número:2
Página de inicio:364
Página de fin:382
DOI: http://dx.doi.org/10.1112/jlms/jdt067
Título revista:Journal of the London Mathematical Society
Título revista abreviado:J. Lond. Math. Soc.
ISSN:00246107
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00246107_v89_n2_p364_DelPezzo

Referencias:

  • Alessandrini, G., Critical points of solutions to the p-Laplace equation in dimension two (1987) Boll. Unione Mat. Ital. Sez. A, 7 (1), pp. 239-246
  • Armstrong, S.N., Silvestre, L., Unique continuation for fully nonlinear elliptic equations (2011) Math. Res. Lett, 18, pp. 921-926
  • Bojarski, B., Iwaniec, T., P-harmonic equation and quasiregular mappings Partial differential equations (Warsaw 1984) (1987) Banach Center Publications, 19, pp. 25-38. , PWN, Warsaw
  • Garofalo, N., Lin, F.-H., Unique continuation for elliptic operators: A geometric-variational approach (1987) Comm. Pure Appl. Math, 40, pp. 347-366
  • Granlund, S., Marola, N., On the problem of unique continuation for the p-Laplace equation (2011) Preprint, , http://www.helsinki.fi/?marola/julkaisuja/uniquecont.pdf
  • Granlund, S., Marola, N., On a frequency function approach to the unique continuation principle (2012) Expo. Math, 30, pp. 154-167
  • Hormander, L., Pseudodifferential operators the analysis of linear partial differential operators III (1985) Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], 274. , Springer, Berlin
  • Jerison, D., Kenig, E.C., Unique continuation and absence of positive eigenvalues for Schr̈odinger operators (1985) Ann. of Math., 2 (121), pp. 463-494. , With an appendix by E M. Stein
  • Kaufman, R., Llorente, J.G., Wu, J.-M., Nonlinear harmonic measures on trees (2003) Ann. Acad. Sci. Fenn. Math, 28, pp. 279-302
  • Kaufman, R., Wu, J.-M., Fatou theorem of p-harmonic functions on trees (2000) Ann. Probab, 28, pp. 1138-1148
  • Koch, H., Tataru, D., Recent Results on Unique Continuation for Second Order Elliptic Equations. Carleman Estimates and Applications to Uniqueness and Control Theory (Cortona 1999) (2001) Progress in Nonlinear Differential Equations and Their Applications, 46, pp. 73-84. , Birkhauser Boston, MA
  • Koch, H., Tataru, D., Sharp counterexamples in unique continuation for second order elliptic equations (2002) J. Reine Angew. Math, 542, pp. 133-146
  • Maitra, A., Sudderth, W., Finitely additive and measurable stochastic games (1993) Internat. J. Game Theory, 22, pp. 201-223
  • Maitra, A., Sudderth, W., Discrete gambling and stochastic games (1996) Applications of Mathematics, 32. , Springer, New York New York
  • Manfredi, J.J., P-harmonic functions in the plane (1988) Proc. Amer. Math. Soc, 103, pp. 473-479
  • Manfredi, J.J., Parviainen, M., Rossi, J.D., Dynamic programming principle for tug-of-war games with noise (2012) ESAIM Control Optim. Calc. Var, 18, pp. 81-90
  • Manfredi, J.J., Parviainen, M., Rossi, J.D., On the definition and properties of p-harmonious functions (2012) Ann. Sc. Norm. Super. Pisa Cl. Sci., 5 (11), pp. 215-241
  • Martio, O., Counterexamples for unique continuation (1988) Manuscripta Math, 60, pp. 21-47
  • Peres, Y., Schramm, O., Sheffield, S., Wilson, D., Tug-of-war and the infinity Laplacian (2009) J. Amer. Math. Soc, 22, pp. 167-210
  • Sviridov, A.P., (2010) Elliptic Equations in Graphs Via Stochastic Games, , http://www.pitt.edu/?aps14/EllipEqinGrphviaSG.pdf, PhD Thesis, University of Pittsburgh
  • Wolff, T.H., Note on counterexamples in strong unique continuation problems (1992) Proc. Amer. Math. Soc, 114, pp. 351-356

Citas:

---------- APA ----------
Del Pezzo, L.M., Mosquera, C.A. & Rossi, J.D. (2014) . The unique continuation property for a nonlinear equation on trees. Journal of the London Mathematical Society, 89(2), 364-382.
http://dx.doi.org/10.1112/jlms/jdt067
---------- CHICAGO ----------
Del Pezzo, L.M., Mosquera, C.A., Rossi, J.D. "The unique continuation property for a nonlinear equation on trees" . Journal of the London Mathematical Society 89, no. 2 (2014) : 364-382.
http://dx.doi.org/10.1112/jlms/jdt067
---------- MLA ----------
Del Pezzo, L.M., Mosquera, C.A., Rossi, J.D. "The unique continuation property for a nonlinear equation on trees" . Journal of the London Mathematical Society, vol. 89, no. 2, 2014, pp. 364-382.
http://dx.doi.org/10.1112/jlms/jdt067
---------- VANCOUVER ----------
Del Pezzo, L.M., Mosquera, C.A., Rossi, J.D. The unique continuation property for a nonlinear equation on trees. J. Lond. Math. Soc. 2014;89(2):364-382.
http://dx.doi.org/10.1112/jlms/jdt067