메뉴 건너뛰기




Volumn 360, Issue 1, 2008, Pages 77-101

The infinity Laplacian, aronsson's equation and their generalizations

Author keywords

Aronsson equations; Infinity laplacian; Random evolutions; Tug of war games

Indexed keywords


EID: 54049147343     PISSN: 00029947     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0002-9947-07-04338-3     Document Type: Article
Times cited : (100)

References (23)
  • 1
    • 0011112875 scopus 로고
    • Minimization problems for the functional supx F(x, f(x), f'(x))
    • MR0196551 (33:4738)
    • [A1] G. Aronsson, Minimization problems for the functional supx F(x, f(x), f'(x)), Arkiv für Mate. 6 (1965), 33-53. MR0196551 (33:4738)
    • (1965) Arkiv für Mate , vol.6 , pp. 33-53
    • Aronsson, G.1
  • 2
    • 84950356703 scopus 로고
    • Minimization problems for the functional supx F(x, f(x), f'(x)). II
    • MR0203541 (34:3391)
    • [A2] G. Aronsson, Minimization problems for the functional supx F(x, f(x), f'(x)). II, Arkiv für Mate. 6 (1966), 409-431. MR0203541 (34:3391)
    • (1966) Arkiv für Mate , vol.6 , pp. 409-431
    • Aronsson, G.1
  • 3
    • 0001457134 scopus 로고
    • Extension of functions satisfying Lipschitz conditions
    • MR0217665 (36:754)
    • [A3] G. Aronsson, Extension of functions satisfying Lipschitz conditions, Arkiv für Mate. 6 (1967), 551-561. MR0217665 (36:754)
    • (1967) Arkiv für Mate , vol.6 , pp. 551-561
    • Aronsson, G.1
  • 4
    • 84950356841 scopus 로고
    • yy = 0
    • MR0237962 (38:6239)
    • yy = 0, Arkiv für Mate. 7 (1968), 395-425. MR0237962 (38:6239)
    • (1968) Arkiv für Mate , vol.7 , pp. 395-425
    • G. Aronsson1
  • 5
    • 0040322556 scopus 로고
    • Minimization problems for the functional supx F(x, f(x), f'(x)). III
    • MR0240690 (39:2035)
    • [A5] G. Aronsson, Minimization problems for the functional supx F(x, f(x), f'(x)). III, Arkiv für Mate. 7 (1969), 509-512. MR0240690 (39:2035)
    • (1969) Arkiv für Mate , vol.7 , pp. 509-512
    • Aronsson, G.1
  • 6
    • 13844298388 scopus 로고    scopus 로고
    • A tour of the theory of absolutely minimizing functions
    • DOI 10.1090/S0273-0979-04-01035-3, PII S0273097904010353
    • [A-C-J] G. Aronsson, M. Crandall and P. Juutinen, A tour of the theory of absolutely minimizing functions, Bull. Amer. Math. Soc. (N.S.), American Mathematical Society. Bulletin. New Series, 41 (2004), 439-505. MR2083637 (2005k:35159) (Pubitemid 40251281)
    • (2004) Bulletin of the American Mathematical Society , vol.41 , Issue.4 , pp. 439-505
    • Aronsson, G.1    Crandall, M.G.2    Juutinen, P.3
  • 7
    • 0038379256 scopus 로고    scopus 로고
    • Viscosity solutions and analysis in L∞
    • Dordrecht. MR1695005 (2001c:49045)
    • [B] E. N. Barron, Viscosity solutions and analysis in L∞, in Nonlinear Analysis, Differential Equations and Control, Dordrecht 1999, 1-60. MR1695005 (2001c:49045)
    • (1999) Nonlinear Analysis, Differential Equations and Control , pp. 1-60
    • Barron, E.N.1
  • 8
    • 0035631814 scopus 로고    scopus 로고
    • The Euler equation and absolute minimizers of L∞ functionals
    • [B-J-W] E. N. Barron, R. Jensen and C. Wang, The Euler equation and absolute minimizers of L∞ functionals, Arch. Rational Mech. Analysis 157 (2001), 255-283. MR1831173 (2002m:49006) (Pubitemid 33584485)
    • (2001) Archive for Rational Mechanics and Analysis , vol.157 , Issue.4 , pp. 255-283
    • Barron, E.N.1    Jensen, R.R.2    Wang, C.Y.3
  • 9
    • 0011655918 scopus 로고
    • Convergence and approximation of semigroups of nonlinear operators in Banach spaces
    • MR0293452 (45:2529)
    • [B-P] H. Brezis and A. Pazy, Convergence and approximation of semigroups of nonlinear operators in Banach spaces, J. Functional Analysis 9 (1972), 63-74. MR0293452 (45:2529)
    • (1972) J. Functional Analysis , vol.9 , pp. 63-74
    • Brezis, H.1    Pazy, A.2
  • 10
    • 84972499852 scopus 로고
    • Uniqueness and existence of viscosity solutions of generalized mean curvature flow equations
    • MR1100211 (93a:35093)
    • [C-G-G] Y. G. Chen, Y. Giga and S. Goto, Uniqueness and existence of viscosity solutions of generalized mean curvature flow equations, Journal of Differential Geometry 33 (1991), 749-786. MR1100211 (93a:35093)
    • (1991) Journal of Differential Geometry , vol.33 , pp. 749-786
    • Chen, Y.G.1    Giga, Y.2    Goto, S.3
  • 11
    • 84967708673 scopus 로고
    • User's guide to viscosity solutions of second order partial differential equations
    • MR1118699 (92j:35050)
    • [C-I-L] M. G. Crandall, H. Ishii and P.-L. Lions, User's guide to viscosity solutions of second order partial differential equations, Bulletin American Math. Soc., 27 (1992), 1-67. MR1118699 (92j:35050)
    • (1992) Bulletin American Math. Soc. , vol.27 , pp. 1-67
    • Crandall, M.G.1    Ishii, H.2    Lions, P.-L.3
  • 12
    • 84971110219 scopus 로고
    • The perturbed test function method for viscosity solutions of nonlinear PDE
    • MR1007533 (91c:35017)
    • [E1] L. C. Evans, The perturbed test function method for viscosity solutions of nonlinear PDE, Proc. Royal Society of Edinburgh 111A (1989), 359-375. MR1007533 (91c:35017)
    • (1989) Proc. Royal Society of Edinburgh 111A , pp. 359-375
    • Evans, L.C.1
  • 13
    • 77950942461 scopus 로고    scopus 로고
    • Regularity for fully nonlinear elliptic PDE and mean curvature motion (survey paper)
    • edited by I. Capuzzo-Dolcetta and P.-L. Lions, Lecture Notes in Mathematics 1660, Springer. MR1462701 (98f:35046)
    • [E2] L. C. Evans, Regularity for fully nonlinear elliptic PDE and mean curvature motion (survey paper), in Viscosity Solutions and Applications, edited by I. Capuzzo-Dolcetta and P.-L. Lions, Lecture Notes in Mathematics 1660, Springer, 1997. MR1462701 (98f:35046)
    • (1997) Viscosity Solutions and Applications
    • Evans, L.C.1
  • 14
    • 84972518016 scopus 로고
    • Motion of level sets by mean curvature I
    • MR1100206 (92h:35097)
    • [E-S] L. C. Evans and J. Spruck, Motion of level sets by mean curvature I, Journal of Differential Geometry 33 (1991), 635-681. MR1100206 (92h:35097)
    • (1991) Journal of Differential Geometry , vol.33 , pp. 635-681
    • Evans, L.C.1    Spruck, J.2
  • 15
    • 0003200789 scopus 로고
    • Functional integration and partial differential equations
    • MR0833742 (87g:60066) Princeton University Press
    • [F] M. Friedlin, Functional Integration and Partial Differential Equations, Princeton University Press, Volume 109, Annals of Mathematics, 1985. MR0833742 (87g:60066)
    • (1985) Annals of Mathematics , vol.109
    • Friedlin, M.1
  • 16
    • 21144476154 scopus 로고
    • Uniqueness of Lipschitz extensions minimizing the sup-norm of the gradient
    • MR1218686 (94g:35063)
    • [J] R. Jensen, Uniqueness of Lipschitz extensions minimizing the sup-norm of the gradient, Arch. Rational Mech. Analysis 123 (1993), 51-74. MR1218686 (94g:35063)
    • (1993) Arch. Rational Mech. Analysis , vol.123 , pp. 51-74
    • Jensen, R.1
  • 22
    • 0344118909 scopus 로고    scopus 로고
    • Weak solutions for equations defined by accretive operators. I
    • [P] M. Portilheiro, Weak solutions for equations defined by accretive operators I, Proceedings Royal Soc Edinburgh 133A (2003), 1193-1207. MR2018332 (2004j:47130) (Pubitemid 37480566)
    • (2003) Royal Society of Edinburgh - Proceedings A , vol.133 , Issue.5 , pp. 1193-1207
    • Portilheiro, M.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.