Abstract
In this paper, we study asymptotic behavior of solutions to obstacle problems for p-Laplacians as
Funding source: Sapienza Universitá di Roma
Award Identifier / Grant number: RM11715C7D9096AD
Funding statement: The authors are members of GNAMPA (INdAM) and are partially supported by Grant Ateneo “Sapienza” 2017.
References
[1] J. Andersson, E. Lindgren and H. Shahgholian, Optimal regularity for the obstacle problem for the p-Laplacian, J. Differential Equations 259 (2015), no. 6, 2167–2179. 10.1016/j.jde.2015.03.019Search in Google Scholar
[2] G. Aronsson, M. G. Crandall and P. Juutinen, A tour of the theory of absolutely minimizing functions, Bull. Amer. Math. Soc. (N. S.) 41 (2004), no. 4, 439–505. 10.1090/S0273-0979-04-01035-3Search in Google Scholar
[3]
T. Bhattacharya, E. DiBenedetto and J. Manfredi,
Limits as
[4] P. Blanc, J. V. da Silva and J. D. Rossi, A limiting free boundary problem with gradient constraint and tug-of-war games, Ann. Mat. Pura Appl. (4) 198 (2019), no. 4, 1441–1469. 10.1007/s10231-019-00825-0Search in Google Scholar
[5] G. Bouchitté, G. Buttazzo and L. De Pascale, A p-Laplacian approximation for some mass optimization problems, J. Optim. Theory Appl. 118 (2003), no. 1, 1–25. 10.1023/A:1024751022715Search in Google Scholar
[6] F. Camilli, R. Capitanelli and M. A. Vivaldi, Absolutely minimizing Lipschitz extensions and infinity harmonic functions on the Sierpinski gasket, Nonlinear Anal. 163 (2017), 71–85. 10.1016/j.na.2017.07.005Search in Google Scholar
[7] R. Capitanelli and S. Fragapane, Asymptotics for quasilinear obstacle problems in bad domains, Discrete Contin. Dyn. Syst. Ser. S 12 (2019), no. 1, 43–56. 10.3934/dcdss.2019003Search in Google Scholar
[8] R. Capitanelli, S. Fragapane and M. A. Vivaldi, Regularity results for p-Laplacians in pre-fractal domains, Adv. Nonlinear Anal. 8 (2019), no. 1, 1043–1056. 10.1515/anona-2017-0248Search in Google Scholar
[9] R. Capitanelli and M. A. Vivaldi, FEM for quasilinear obstacle problems in bad domains, ESAIM Math. Model. Numer. Anal. 51 (2017), no. 6, 2465–2485. 10.1051/m2an/2017033Search in Google Scholar
[10] L. C. Evans and W. Gangbo, Differential equations methods for the Monge–Kantorovich mass transfer problem, Mem. Amer. Math. Soc. 137 (1999), no. 653, 1–66. 10.1090/memo/0653Search in Google Scholar
[11] M. Feldman and R. J. McCann, Uniqueness and transport density in Monge’s mass transportation problem, Calc. Var. Partial Differential Equations 15 (2002), no. 1, 81–113. 10.1007/s005260100119Search in Google Scholar
[12] A. Figalli, B. Krummel and X. Ros-Oton, On the regularity of the free boundary in the p-Laplacian obstacle problem, J. Differential Equations 263 (2017), no. 3, 1931–1945. 10.1016/j.jde.2017.03.035Search in Google Scholar
[13] H. Ishii and P. Loreti, Limits of solutions of p-Laplace equations as p goes to infinity and related variational problems, SIAM J. Math. Anal. 37 (2005), no. 2, 411–437. 10.1137/S0036141004432827Search in Google Scholar
[14] R. Jensen, Uniqueness of Lipschitz extensions: minimizing the sup norm of the gradient, Arch. Ration. Mech. Anal. 123 (1993), no. 1, 51–74. 10.1007/BF00386368Search in Google Scholar
[15] P. Juutinen, M. Parviainen and J. D. Rossi, Discontinuous gradient constraints and the infinity Laplacian, Int. Math. Res. Not. IMRN 2016 (2016), no. 8, 2451–2492. 10.1093/imrn/rnv214Search in Google Scholar
[16] K. Kuratowski, Topology. Vol. I and II, Academic Press, New York, 1966. Search in Google Scholar
[17] G. Lu and P. Wang, Inhomogeneous infinity Laplace equation, Adv. Math. 217 (2008), no. 4, 1838–1868. 10.1016/j.aim.2007.11.020Search in Google Scholar
[18] J. M. Mazón, J. D. Rossi and J. Toledo, Mass transport problems for the Euclidean distance obtained as limits of p-Laplacian type problems with obstacles, J. Differential Equations 256 (2014), no. 9, 3208–3244. 10.1016/j.jde.2014.01.039Search in Google Scholar
[19] J. D. Rossi, E. V. Teixeira and J. M. Urbano, Optimal regularity at the free boundary for the infinity obstacle problem, Interfaces Free Bound. 17 (2015), no. 3, 381–398. 10.4171/IFB/347Search in Google Scholar
[20] G. M. Troianiello, Elliptic Differential Equations and Obstacle Problems, Univ. Ser. Math., Plenum Press, New York, 1987. 10.1007/978-1-4899-3614-1Search in Google Scholar
[21] C. Villani, Optimal Transport. Old and New, Grundlehren Math. Wiss. 338, Springer, Berlin, 2009, 10.1007/978-3-540-71050-9Search in Google Scholar
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Articles in the same Issue
- Frontmatter
- Prescribing Morse scalar curvatures: Critical points at infinity
- Convergence of dynamic programming principles for the p-Laplacian
- Connected perimeter of planar sets
- Constant Q-curvature metrics on conic 4-manifolds
- Limit of 𝑝-Laplacian obstacle problems
- Long-time behaviour of solutions to an evolution PDE with nonstandard growth
Articles in the same Issue
- Frontmatter
- Prescribing Morse scalar curvatures: Critical points at infinity
- Convergence of dynamic programming principles for the p-Laplacian
- Connected perimeter of planar sets
- Constant Q-curvature metrics on conic 4-manifolds
- Limit of 𝑝-Laplacian obstacle problems
- Long-time behaviour of solutions to an evolution PDE with nonstandard growth