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Volumn 177, Issue 2, 2009, Pages 415-461

Some new monotonicity formulas and the singular set in the lower dimensional obstacle problem

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EID: 67650683389     PISSN: 00209910     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00222-009-0188-4     Document Type: Article
Times cited : (140)

References (21)
  • 1
    • 0005332561 scopus 로고
    • Dirichlet's problem for multiple valued functions and the regularity of mass minimizing integral currents
    • North-Holland Amsterdam
    • Almgren, F.J. Jr.: Dirichlet's problem for multiple valued functions and the regularity of mass minimizing integral currents. In: Minimal Submanifolds and Geodesics. Proc. Japan-United States Sem., Tokyo, 1977, pp. 1-6. North-Holland, Amsterdam (1979)
    • (1979) Minimal Submanifolds and Geodesics Proc. Japan-United States Sem. Event Tokyo 1977 , pp. 1-6
    • Almgren, Jr.F.J.1
  • 2
    • 84967774571 scopus 로고
    • Variational problems with two phases and their free boundaries
    • H.W. Alt L.A. Caffarelli A. Friedman 1984 Variational problems with two phases and their free boundaries Trans. Am. Math. Soc. 282 2 431 461
    • (1984) Trans. Am. Math. Soc. , vol.282 , Issue.2 , pp. 431-461
    • Alt, H.W.1    Caffarelli, L.A.2    Friedman, A.3
  • 3
    • 37549032410 scopus 로고    scopus 로고
    • Optimal regularity of lower dimensional obstacle problems
    • Kraev. Zadachi Mat. Fiz. i Smezh. Vopr. Teor. Funkts. [34], 226 (English, with English and Russian summaries); English transl. J. Math. Sci. (NY) 132(3), 274-284 (2006)
    • I. Athanasopoulos L.A. Caffarelli 2004 Optimal regularity of lower dimensional obstacle problems Zap. Naucn. Semin. St.-Peterb. Otd. Mat. Inst. Steklova (POMI) 310 35 49 66 Kraev. Zadachi Mat. Fiz. i Smezh. Vopr. Teor. Funkts. [34], 226 (English, with English and Russian summaries); English transl. J. Math. Sci. (NY) 132(3), 274-284 (2006)
    • (2004) Zap. Naucn. Semin. St.-Peterb. Otd. Mat. Inst. Steklova (POMI) , vol.310 , Issue.35 , pp. 49-66
    • Athanasopoulos, I.1    Caffarelli, L.A.2
  • 4
    • 43749087546 scopus 로고    scopus 로고
    • The structure of the free boundary for lower dimensional obstacle problems
    • I. Athanasopoulos L.A. Caffarelli S. Salsa 2008 The structure of the free boundary for lower dimensional obstacle problems Am. J. Math. 130 2 485 498
    • (2008) Am. J. Math. , vol.130 , Issue.2 , pp. 485-498
    • Athanasopoulos, I.1    Caffarelli, L.A.2    Salsa, S.3
  • 5
    • 0039084933 scopus 로고
    • Further regularity for the Signorini problem
    • L.A. Caffarelli 1979 Further regularity for the Signorini problem Commun. Partial Differ. Equ. 4 9 1067 1075
    • (1979) Commun. Partial Differ. Equ. , vol.4 , Issue.9 , pp. 1067-1075
    • Caffarelli, L.A.1
  • 6
    • 1842766318 scopus 로고    scopus 로고
    • The obstacle problem revisited
    • L.A. Caffarelli 1998 The obstacle problem revisited J. Fourier Anal. Appl. 4 4-5 383 402
    • (1998) J. Fourier Anal. Appl. , vol.4 , Issue.45 , pp. 383-402
    • Caffarelli, L.A.1
  • 7
    • 0005309049 scopus 로고
    • Asymptotic behaviour of free boundaries at their singular points
    • L.A. Caffarelli N.M. Rivière 1977 Asymptotic behaviour of free boundaries at their singular points Ann. Math. (2) 106 2 309 317
    • (1977) Ann. Math. (2) , vol.106 , Issue.2 , pp. 309-317
    • Caffarelli, L.A.1    Rivière, N.M.2
  • 8
    • 37849049246 scopus 로고    scopus 로고
    • Regularity estimates for the solution and the free boundary of the obstacle problem for the fractional Laplacian
    • L. Caffarelli S. Salsa L. Silvestre 2008 Regularity estimates for the solution and the free boundary of the obstacle problem for the fractional Laplacian Invent. Math. 171 2 425 461
    • (2008) Invent. Math. , vol.171 , Issue.2 , pp. 425-461
    • Caffarelli, L.1    Salsa, S.2    Silvestre, L.3
  • 9
    • 34548348805 scopus 로고    scopus 로고
    • An extension problem related to the fractional Laplacian
    • L. Caffarelli L. Silvestre 2007 An extension problem related to the fractional Laplacian Commun. Partial Differ. Equ. 32 7-9 1245 1260
    • (2007) Commun. Partial Differ. Equ. , vol.32 , Issue.79 , pp. 1245-1260
    • Caffarelli, L.1    Silvestre, L.2
  • 14
    • 84990604274 scopus 로고
    • Unique continuation for elliptic operators: A geometric-variational approach
    • N. Garofalo F.-H. Lin 1987 Unique continuation for elliptic operators: a geometric-variational approach Commun. Pure Appl. Math. 40 3 347 366
    • (1987) Commun. Pure Appl. Math. , vol.40 , Issue.3 , pp. 347-366
    • Garofalo, N.1    Lin, F.-H.2
  • 16
    • 84867974824 scopus 로고    scopus 로고
    • On the number of singularities for the obstacle problem in two dimensions
    • R. Monneau 2003 On the number of singularities for the obstacle problem in two dimensions J. Geom. Anal. 13 2 359 389
    • (2003) J. Geom. Anal. , vol.13 , Issue.2 , pp. 359-389
    • Monneau, R.1
  • 18
    • 33751514593 scopus 로고    scopus 로고
    • Regularity of the obstacle problem for a fractional power of the laplace operator
    • DOI 10.1002/cpa.20153
    • L. Silvestre 2007 Regularity of the obstacle problem for a fractional power of the Laplace operator Commun. Pure Appl. Math. 60 1 67 112 (Pubitemid 44832316)
    • (2007) Communications on Pure and Applied Mathematics , vol.60 , Issue.1 , pp. 67-112
    • Silvestre, L.1
  • 19
    • 77954190865 scopus 로고
    • On the regularity of solutions of variational inequalities
    • (Russian); English transl., Russ. Math. Surv. 42(6), 191-219 (1987)
    • N.N. Ural'tseva 1987 On the regularity of solutions of variational inequalities Usp. Mat. Nauk 42 6 151 174 (Russian); English transl., Russ. Math. Surv. 42(6), 191-219 (1987)
    • (1987) Usp. Mat. Nauk , vol.42 , Issue.6 , pp. 151-174
    • Ural'Tseva, N.N.1
  • 20
    • 0033239032 scopus 로고    scopus 로고
    • A homogeneity improvement approach to the obstacle problem
    • G.S. Weiss 1999 A homogeneity improvement approach to the obstacle problem Invent. Math. 138 1 23 50
    • (1999) Invent. Math. , vol.138 , Issue.1 , pp. 23-50
    • Weiss, G.S.1
  • 21
    • 77956456169 scopus 로고
    • Analytic extensions of differentiable functions defined in closed sets
    • H. Whitney 1934 Analytic extensions of differentiable functions defined in closed sets Trans. Am. Math. Soc. 36 1 63 89
    • (1934) Trans. Am. Math. Soc. , vol.36 , Issue.1 , pp. 63-89
    • Whitney, H.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.