NONLINEAR MEAN-VALUE FORMULAS on FRACTAL SETS

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In this paper we study the solutions to nonlinear mean-value formulas on fractal sets. We focus on the mean-value problem 1 2maxq Vm,p{f(q)} + 1 2minq Vm,p{f(q)}-f(p) = 0 in the Sierpiński gasket with prescribed values f(p1), f(p2) and f(p3) at the three vertices of the first triangle. For this prob...

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Autor principal: Navarro, J.C
Otros Autores: Rossi, J.D
Formato: Capítulo de libro
Lenguaje:Inglés
Publicado: World Scientific Publishing Co. Pte Ltd 2018
Acceso en línea:Registro en Scopus
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100 1 |a Navarro, J.C. 
245 1 0 |a NONLINEAR MEAN-VALUE FORMULAS on FRACTAL SETS 
260 |b World Scientific Publishing Co. Pte Ltd  |c 2018 
270 1 0 |m Rossi, J.D.; Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires Ciudad Universitaria-Pabellón iArgentina; email: jrossi@dm.uba.ar 
506 |2 openaire  |e Política editorial 
504 |a Manfredi, J.J., Parviainen, M., Rossi, J.D., An asymptotic mean value characterization for pharmonic functions (2010) Proc. Am. Math. Soc., 138, pp. 881-889 
504 |a Hartenstine, D., Rudd, M., Asymptotic statistical characterizations of p-harmonic functions of two variables (2011) Rocky Mt. J. Math., 41 (2), pp. 493-504 
504 |a Hartenstine, D., Rudd, M., Statistical functional equations and p-harmonious functions (2013) Adv. Nonlinear Stud., 13 (1), pp. 191-207 
504 |a 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., 11 (2), pp. 215-241 
504 |a 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 
504 |a 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 
504 |a Oberman, A., Finite difference methods for the infinity Laplace and p-Laplace equations (2013) J. Comput. Appl. Math., 254, pp. 65-80 
504 |a Oberman, A., A convergent difference scheme for the infinity Laplacian: Construction of absolutely minimizing Lipschitz extensions (2005) Math. Comput., 74 (251), pp. 1217-1230 
504 |a Peres, Y., Schramm, O., Sheffield, S., Wilson, D., Tug-of-war and the infinity Laplacian (2009) J. Am. Math. Soc., 22 (1), pp. 167-210 
504 |a Peres, Y., Schramm, O., Sheffield, S., Wilson, D.B., Tugof-war and the infinity Laplacian (2011) Selected Works of Oded Schramm, Selected Works in Probability and Statisitcs, 1-2, pp. 595-638. , Springer, New York 
504 |a Rossi, J.D., Tug-of-war games and PDEs (2011) Proc. R. Soc. Edinb. A, 141 (2), pp. 319-369 
504 |a Alvarez, V., Rodríguez, J.M., Yakubovich, D.V., Estimates for nonlinear harmonic "measures" on trees (2001) Michigan Math. J., 49 (1), pp. 47-64 
504 |a Del Pezzo, L.M., Mosquera, C.A., Rossi, J.D., The unique continuation property for a nonlinear equation on trees (2014) J. Lond. Math. Soc., 89, pp. 364-382 
504 |a Del Pezzo, L.M., Mosquera, C.A., Rossi, J.D., Estimates for nonlinear harmonic measures on trees (2014) Bull. Braz. Math. Soc., 45 (3), pp. 405-432 
504 |a Kaufman, R., Llorente, J.G., Wu, J.-M., Nonlinear harmonic measures on trees (2003) Ann. Acad. Sci. Fenn. Math., 28 (2), pp. 279-302 
504 |a Kaufman, R., Wu, J.-M., Fatou theorem of pharmonic functions on trees (2000) Ann. Probab., 28 (3), pp. 1138-1148 
504 |a Manfredi, J.J., Oberman, A., Sviridov, A., Nonlinear elliptic partial differential equations and pharmonic functions on graphs (2015) Diff. Integral Eqs., 28 (1-2), pp. 79-102 
504 |a Sviridov, A.P., (2011) Elliptic Equations in Graphs Via Stochastic Games, , Ph.D. thesis, University of Pittsburgh, Pittsburgh, PA 
504 |a Sviridov, A.P., P-harmonious functions with drift on graphs via games (2011) Electron. J. Diff. Eqs., 2011, pp. 1141-11411 
504 |a Strichartz, R.S., (2006) Differential Equations on Fractals: A Tutorial, , Princeton University Press 
504 |a Li, P.-H., Ryder, N., Strichartz, R.S., Ugurcan, B., Extensions and their minimizations on the Sierpiński gasket (2014) Potential Anal., 41 (4), pp. 1167-1201 
504 |a Owen, J., Strichartz, R.S., Boundary value problems for harmonic functions on a domain in the Sierpinski gasket (2012) Indiana Univ. Math. J., 61 (1), pp. 319-335 
504 |a Barlow, M.T., Diffusion on fractals (1998) Lectures on Probability Theory and Statistics, Lectures Notes in Mathematics, 1690, pp. 1-114. , Springer, Berlin 
504 |a Qiu, H., Strichartz, R.S., Mean value properties of harmonic functions on Sierpiński gasket type fractals (2013) J. Fourier Anal. Appl., 19 (5), pp. 943-966 
504 |a Camilli, F., Capitanelli, R., Vivaldi, M.A., Absolutely minimizing Lipschitz extensions and infinity harmonic functions on the Sierpiński gasket (2017) Nonlinear Anal., 163, pp. 71-85 
504 |a Camilli, F., Capitanelli, R., Marchi, C., Eikonal equations on the Sierpiński gasket (2016) Math. Ann., 364 (3-4), pp. 1167-1188 
504 |a Kigami, J., (2001) Analysis on Fractals, , Cambridge University Press, Cambridge 
504 |a Maitra, A.P., Sudderth, W.D., (1996) Discrete Gambling and Stochastic Games, Stochastic Modelling and Applied Probability, 32. , Springer-Verlag 
504 |a Wolff, T.H., Gap series constructions for the p-Laplacian (2007) J. Anal. Math., 102, pp. 371-394 
520 3 |a In this paper we study the solutions to nonlinear mean-value formulas on fractal sets. We focus on the mean-value problem 1 2maxq Vm,p{f(q)} + 1 2minq Vm,p{f(q)}-f(p) = 0 in the Sierpiński gasket with prescribed values f(p1), f(p2) and f(p3) at the three vertices of the first triangle. For this problem we show existence and uniqueness of a continuous solution and analyze some properties like the validity of a comparison principle, Lipschitz continuity of solutions (regularity) and continuous dependence of the solution with respect to the prescribed values at the three vertices of the first triangle. © 2018 World Scientific Publishing Company.  |l eng 
536 |a Detalles de la financiación: MTM2010-18128, MTM2011-27998 
536 |a Detalles de la financiación: This work was supported by the MEC Projects MTM2010-18128 and MTM2011-27998 (Spain). 
593 |a Departamento de Análisis Matemático, Universidad de Alicante, Apartado de Correos 99, Alicante, E-03080, Spain 
593 |a Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires Ciudad Universitaria-Pabellón i, Buenos Aires, C1428EGA, Argentina 
690 1 0 |a FRACTAL SETS 
690 1 0 |a MEAN-VALUE FORMULAS 
690 1 0 |a GEOMETRY 
690 1 0 |a COMPARISON PRINCIPLE 
690 1 0 |a CONTINUOUS DEPENDENCE 
690 1 0 |a EXISTENCE AND UNIQUENESS 
690 1 0 |a FRACTAL SETS 
690 1 0 |a LIPSCHITZ CONTINUITY 
690 1 0 |a MEAN VALUES 
690 1 0 |a FRACTALS 
700 1 |a Rossi, J.D. 
773 0 |d World Scientific Publishing Co. Pte Ltd, 2018  |g v. 26  |k n. 6  |p Fractals  |x 0218348X  |w (AR-BaUEN)CENRE-1709  |t Fractals 
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