Overdetermined boundary value problems for the ∞-Laplacian

International Mathematics Research Notices

Volumn 2011, Issue 2, 2011, Pages 237-247

  Buttazzo, Giuseppe ^a   Kawohl, Bernd ^b  

^a UNIVERSITY OF PISA   (Italy)

^b UNIVERSITY OF COLOGNE   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 79251488830     PISSN: 10737928     EISSN: 16870247     Source Type: Journal    
DOI: 10.1093/imrn/rnq071     Document Type: Article

References (20)

1. Bhattacharya, T., E. DiBenedetto, and J. Manfredi. "Limits as p → of ∞ Δ pup = f and related extremal problems." Rendiconti del Seminario Matematico Università e Politecnico di Torino, Special Issue (1991): 15-68.
2. Crandall, M., H. Ishii, and P.-L. Lions. "User's guide to viscosity solutions of second order partial differential equations." Bulletin of the American Mathematical Society 27 (1992): 1-67.
3. Crasta, G., I. Fragal̀a, and F. Gazzola. "On the role of energy convexity in the web function approximation." Nonlinear Differential Equations Applications 12 (2005): 93-109.
4. Crasta, G., and A. Malusa. "The distance function from the boundary in a Minkowski space." Transactions of the American Mathematical Society 359 (2007): 5725-59.
5. Farina, A., and B. Kawohl. "Remarks on an overdetermined boundary value problem." Calculus of Variations and Partial Differential Equations 89 (2008): 351-7.
6. Garofalo, N., and J. L. Lewis. "A symmetry result related to some overdetermined boundary value problems." American Journal of Mathematics 111 (1989): 9-33.
7. Juutinen, P. "Minimization problems for Lipschitz functions via viscosity solutions." Annales Academiæ Scientiarium Fennicæ Mathematica Dissertationes 115 (1998).
8. Juutinen, P., P. Lindqvist, and J. Manfredi. "The ∞-eigenvalue problem." Archive for Rational Mechanics and Analysis 148 (1999): 89-105.
9. Juutinen, P., and B. Kawohl. "On the evolution governed by the infinity Laplacian." Mathematische Annalen 335 (2006): 819-51.
10. Kawohl, B. "On a family of torsional creep problems." Journal für die Reine und Angewandte Mathematik 410 (1990): 1-22.
11. Li, Y. Y., and L. Nirenberg. "Regularity of the distance function to the boundary." Rendiconti della Accademia Nazionale delle Scienze detta dei XL Memorie di Matematica e Applicazioni 29 (2005): 25-264.
12. Lu, G., and P. Wang. "A PDE perspective of the normalized infinity Laplacian." Communications in Partial Differential Equations 33 (2008): 1788-817.
13. Lu, G., and P. Wang. "A uniqueness theorem for degenerate elliptic equations." In Conference on Geometric Methods in PDE's, edited by G. Citti, A. Montanari, A. Pascucci, S. Polidoro, 207-222. On the Occasion of 65th Birthday of Ermanno Lanconelli (Bologna, May 27-30, 2008). Lecture Notes of Seminario Interdisciplinare di Matematica. Potenza, Italy: Universit ̀a degli Studi della Basilicata.
14. Mantegazza, C., and A. C. Mennucci. "Hamilton-Jacobi equations and distance functions on Riemannian manifolds." Applied Mathematics and Optimization 47 (2003): 1-25.
15. Peres, Y., and S. Sheffield. "Tug-of-war with noise: a game-theoretic view of the p-Laplacian." Duke Mathematical Journal 145 (2008): 91-120.
16. Peres, Y., O. Schramm, S. Sheffield, and D. Wilson. "Tug-of-war and the infinity Laplacian." Journal of the American Mathematical Society 22 (2009): 167-210.
17. Serrin, J. "A symmetry problem in potential theory." Archive for Rational Mechanics and Analysis 43 (1971): 304-18.
18. Weinberger, H. "Remark on the preceding paper of Serrin." Archive for Rational Mechanics and Analysis 43 (1971): 319-20.
19. Yu, Y. "Some properties of the ground states of the infinity Laplacian." Indiana University Mathematics Journal 56 (2007): 947-64.
20. Yu, Y. "Uniqueness of values of Aronsson operators and running costs in "tug-of-war" games." Annales de l'Institut Henri Poincaŕ e, Analyse Linaire 26 (2009): 1299-308.