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Abstract:

Fix two differential operators L1 and L2, and define a sequence of functions inductively by considering u1 as the solution to the Dirichlet problem for an operator L1 and then un as the solution to the obstacle problem for an operator Li ( i=1,2${i=1,2}$ alternating them) with obstacle given by the previous term un-1 in a domain Ω and a fixed boundary datum g on Ω${\\partial \\Omega }$ . We show that in this way we obtain an increasing sequence that converges uniformly to a viscosity solution to the minimal operator associated with L1 and L2, that is, the limit u verifies min{L 1 u,L 2 u}=0${\\min \\lbrace L-1 u, L-2 u \\rbrace =0}$ in Ω with u=g${u=g}$ on Ω${\\partial \\Omega }$ . © 2016 by De Gruyter.

Registro:

Documento: Artículo
Título:Obstacle Problems and Maximal Operators
Autor:Blanc, P.; Pinasco, J.P.; Rossi, J.D.
Filiación:Departmento de Mathematica, FCEyN, Buenos Aires University, Ciudad Universitaria, Pab 1 (1428), Buenos Aires, Argentina
Palabras clave:Dirichlet Boundary Conditions; Maximal Operators; Obstacle Problems
Año:2016
Volumen:16
Número:2
Página de inicio:355
Página de fin:362
DOI: http://dx.doi.org/10.1515/ans-2015-5044
Título revista:Advanced Nonlinear Studies
Título revista abreviado:Adv. Nonlinear Stud.
ISSN:15361365
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_15361365_v16_n2_p355_Blanc

Referencias:

  • Andersson, J., Lindgren, E., Shahgholian, H., (2015) Optimal Regularity for the Obstacle Problem for the P-Laplacian, , http://arxiv.org/abs/1402.4953, preprint
  • Blanc, P., Pinasco, J.P., Rossi, J.D., (2015) Maximal Operators for the P-Laplacian Family, , http://mate.dm.uba.ar/~jrossi/BlancPinascoRossi-sns.pdf, preprint
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  • Daskalopoulos, P., Feehan, P.M.N., (2016) C1,1 Regularity for Degenerate Elliptic Obstacle Problems in Mathematical Finance, , http://arxiv.org/abs/1206.0831, preprint
  • 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
  • Peres, Y., Schramm, O., Sheffield, S., Wilson, D., Tug-of-war and the infinity Laplacian (2009) J. Amer. Math. Soc., 22, pp. 167-210
  • 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
  • Petrosyan, A., Shagholian, H., Uraltseva, N., (2012) Regularity of Free Boundaries in Obstacle Type Problems, , American Mathematical Society Providence
  • Silvestre, L., Regularity of the obstacle problem for a fractional power of the Laplace operator (2007) Comm. Pure Appl. Math., 60 (1), pp. 67-112

Citas:

---------- APA ----------
Blanc, P., Pinasco, J.P. & Rossi, J.D. (2016) . Obstacle Problems and Maximal Operators. Advanced Nonlinear Studies, 16(2), 355-362.
http://dx.doi.org/10.1515/ans-2015-5044
---------- CHICAGO ----------
Blanc, P., Pinasco, J.P., Rossi, J.D. "Obstacle Problems and Maximal Operators" . Advanced Nonlinear Studies 16, no. 2 (2016) : 355-362.
http://dx.doi.org/10.1515/ans-2015-5044
---------- MLA ----------
Blanc, P., Pinasco, J.P., Rossi, J.D. "Obstacle Problems and Maximal Operators" . Advanced Nonlinear Studies, vol. 16, no. 2, 2016, pp. 355-362.
http://dx.doi.org/10.1515/ans-2015-5044
---------- VANCOUVER ----------
Blanc, P., Pinasco, J.P., Rossi, J.D. Obstacle Problems and Maximal Operators. Adv. Nonlinear Stud. 2016;16(2):355-362.
http://dx.doi.org/10.1515/ans-2015-5044