P-harmonic approximation of functions of least gradient

Indiana University Mathematics Journal

Volumn 54, Issue 4, 2005, Pages 1015-1029

  Juutinen, Petri ^a  

^a UNIVERSITY OF JYVÄSKYLÄ   (Finland)

Author keywords

Function of least gradient; p Laplacian

Indexed keywords

EID: 26444473203     PISSN: 00222518     EISSN: None     Source Type: Journal    
DOI: 10.1512/iumj.2005.54.2658     Document Type: Article

References (20)

1. p regularization of the non-parametric minimal surface problem, Ill-Posed Variational Problems and Regularization Techniques (Trier, 1998), Lecture Notes in Econom. and Math. Systems, vol. 477, Springer, Berlin, 1999, pp. 25-34. MR1737310 (2001g:49062)
2. ENRICO BOMBIERI, ENNIO DE GIORGI, and ENRICO GIUSTI, Minimal cones and the Bernstein problem, Invent. Math. 7 (1969), 243-268, http://dx.doi.org/10. 1007/BF01404309. MR0250205 (40 #3445)
3. MARCO CICALESE and CRISTINA TROMBETTI, Asymptotic behaviour of solutions to p-Laplacian equation, Asymptot. Anal. 35 (2003), 27-40. MR2004717 (2005b:35075)
4. MICHAEL G. CRANDALL, HITOSHI ISHII, and PIERRE-LOUIS LIONS, User's guide to viscosity solutions of second order partial differential equations, Bull. Amer. Math. Soc. (N.S.) 27 (1992), 1-67. MR1118699 (92j:35050)
5. 1]., Bull. Amer. Math. Soc. 334 (2002), 1071-1076. MR1911649 (2003e:35082) (French)
6. 1+α local regularity of weak solutions of degenerate elliptic equations, Nonlinear Anal. 7 (1983), 827-850, http://dx.doi.org/10.1016/0362-546X(83)90061-5. MR0709038 (85d:35037)
7. LAWRENCE C. EVANS and JOEL STRUCK, Motion of level sets by mean curvature. I., J. Differential Geom. 33 (1991), 635-681. MR1100206 (92h:35097)
8. DAVID GILBARG and NEIL S. TRUDINGER, Elliptic Partial Differential Equations of Second Order. Reprint of the 1998 edition, Classics in Mathematics, Springer-Verlag, Berlin, 2001, ISBN 3-540-41160-7. MR1814364 (2001k:35004)
9. ENRICO GIUSTI, Minimal Surfaces and Functions of Bounded Variation, Monographs in Mathematics, vol. 80, Birkhäuser Verlag, Basel, 1984, ISBN 0-8176-3153-4. MR0775682 (87a:58041)
10. _, Direct Methods in the Calculus of Variations, World Scientific Publishing Co., Inc., River Edge, NJ, 2003, ISBN 981-238-043-4. MR1962933 (2004g:49003)
11. JUHA HEINONEN, TERO KILPELÄINEN, and OLLI MARTIO, Nonlinear Potential Theory of Degenerate Elliptic Equations, Oxford Mathematical Monographs. Oxford Science Publications, The Clarendon Press, Oxford University Press, New York, 1993, ISBN 0-19-853669-0. MR1207810 (94e:31003)
12. TOM ILMANEN, PETER STERNBERG, and WILLIAM P. ZIEMER, Equilibrium solutions to generalized motion by mean curvature. Dedicated to the memory of Fred Almgren, J. Geom. Anal. 8 (1998), 845-858. MR1731065 (2001b:53087)
13. PETRI JUUTINEN, PETER LINDQVIST, and JUAN J. MANFREDI, On the equivalence of viscosity solutions and weak solutions for a quasi-linear equation, SIAM J. Math. Anal. 33 (2001) (electronic), 699-717, http://dx.doi.org/10.1137/ S0036141000372179. MR1871417 (2002m:35051)
14. BERND KAWOHL, On a family of torsional creep problems, J. Reine Angew. Math. 410 (1990), 1-22. MR1068797 (91h:35126)
15. BERND KAWOHL and V. FRIDMAN, Isoperimetric estimates for the first eigenvalue of the p-Laplace operator and the Cheeger constant, Comment. Math. Univ. Carolin. 44 (2003), 659-667. MR2062882 (2005g:35053)
16. HAROLD PARKS, Explicit determination of area minimizing hypersurfacess, Duke Math. J. 44 (1977), 519-534, http://dx.doi.org/10.1215/S0012-7094-77-04423- 4. MR0458304 (56 #16507)
17. HALSEY L. ROYDEN, Real Analysis, The Macmillan Co., New York, 1963. MR0151555 (27 #1540)
18. PETER STERNBERG, GRAHAM WILLIAMS, and WILLIAM P. ZIEMER, Existence, uniqueness, and regularity for functions of least gradient, J. Reine Angew. Math. 430 (1992), 35-60. MR1172906 (93i:49055)
19. PETER STERNBERG and WILLIAM P. ZIEMER, Generalized motion by curvature with a Dirichlet condition, J. Differential Equations 114 (1994), 580-600, http://dx.doi.org/10.1006/jdeq.1994.1162. MR1303041 (96a:35096)
20. WILLIAM P. ZIEMER, Weakly differentiable functions. Sobolev spaces and functions of bounded variation, Graduate Texts in Mathematics, vol. 120, Springer-Verlag, New York, 1989, ISBN 0-387-97017-7. MR1014685 (91e:46046)