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Volumn 50, Issue 3, 2001, Pages 1077-1112

Sharp results for the regularity and stability of the free boundary in the obstacle problem

Author keywords

Free boundary; Obstacle problem; Regularity; Stability

Indexed keywords


EID: 0039300025     PISSN: 00222518     EISSN: None     Source Type: Journal    
DOI: 10.1512/iumj.2001.50.1906     Document Type: Article
Times cited : (59)

References (28)
  • 1
    • 0000146930 scopus 로고
    • The fluid flow through porous media. Regularity of the free surface
    • H.W. ALT, The fluid flow through porous media. Regularity of the free surface, Manuscripta Math. 21 (1977), no. 3, 255-272.
    • (1977) Manuscripta Math. , vol.21 , Issue.3 , pp. 255-272
    • Alt, H.W.1
  • 2
    • 84990557190 scopus 로고
    • A theorem of real analysis and its application to free boundary problems
    • I. ATHANASOPOULOS AND L.A. CAFFARELLI, A theorem of real analysis and its application to free boundary problems, Comm. Pure Appl. Math. 38 (1985), no. 5, 499-502.
    • (1985) Comm. Pure Appl. Math. , vol.38 , Issue.5 , pp. 499-502
    • Athanasopoulos, I.1    Caffarelli, L.A.2
  • 3
    • 0016038240 scopus 로고
    • The smoothness of solutions to nonlinear variational inequalities
    • H. BRÉZIS AND D. KINDERLEHRER, The smoothness of solutions to nonlinear variational inequalities, Indiana Univ. Math. J. 23 (1973/74), 831-844.
    • (1973) Indiana Univ. Math. J. , vol.23 , pp. 831-844
    • Brézis, H.1    Kinderlehrer, D.2
  • 4
    • 0000409224 scopus 로고
    • The regularity of free boundaries in higher dimensions
    • L.A. CAFFARELLI, The regularity of free boundaries in higher dimensions, Acta Math. 139 (1977), no. 3-4, 155-184.
    • (1977) Acta Math. , vol.139 , Issue.3-4 , pp. 155-184
    • Caffarelli, L.A.1
  • 5
    • 84963451046 scopus 로고
    • Compactness methods in free boundary problems
    • L.A. CAFFARELLI, Compactness methods in free boundary problems, Comm. Partial Differential Equations 5 (1980), no. 4, 427-448.
    • (1980) Comm. Partial Differential Equations , vol.5 , Issue.4 , pp. 427-448
    • Caffarelli, L.A.1
  • 6
    • 0040168632 scopus 로고
    • A remark on the Hausdorff measure of a free boundary, and the convergence of coincidence sets
    • L.A. CAFFARELLI, A remark on the Hausdorff measure of a free boundary, and the convergence of coincidence sets, Boll. Un. Mat. Ital. A (5)18 (1981), no. 1, 109-113.
    • (1981) Boll. Un. Mat. Ital. A (5) , vol.18 , Issue.1 , pp. 109-113
    • Caffarelli, L.A.1
  • 7
    • 1842766318 scopus 로고    scopus 로고
    • The obstacle problem revisited
    • L.A. CAFFARELLI, The obstacle problem revisited, J. Fourier Anal. Appl. 4 (1998), no. 4-5, 383-402.
    • (1998) J. Fourier Anal. Appl. , vol.4 , Issue.4-5 , pp. 383-402
    • Caffarelli, L.A.1
  • 9
    • 0000736848 scopus 로고
    • Boundary behavior of nonnegative solutions of elliptic operators in divergence form
    • L.A. CAFFARELLI, E.B. FABES, S. MORTOLA, AND S. SALSA, Boundary behavior of nonnegative solutions of elliptic operators in divergence form, Indiana Univ. Math. J. 30 (1981), no. 4, 621-640.
    • (1981) Indiana Univ. Math. J. , vol.30 , Issue.4 , pp. 621-640
    • Caffarelli, L.A.1    Fabes, E.B.2    Mortola, S.3    Salsa, S.4
  • 10
    • 51249181477 scopus 로고
    • Potential methods in variational inequalities
    • L.A. CAFFARELLI AND D. KINDERLEHRER, Potential methods in variational inequalities, J. Analyse Math. 37 (1980), 285-295.
    • (1980) J. Analyse Math. , vol.37 , pp. 285-295
    • Caffarelli, L.A.1    Kinderlehrer, D.2
  • 11
    • 0037741792 scopus 로고
    • On the regularity of the solution of a second order variational inequality
    • J. FREHSE, On the regularity of the solution of a second order variational inequality, Boll. Un. Mat. Ital. (4)6 (1972), 312-315.
    • (1972) Boll. Un. Mat. Ital. (4) , vol.6 , pp. 312-315
    • Frehse, J.1
  • 14
    • 0002004980 scopus 로고
    • Boundary behavior of harmonic functions in nontangentially accessible domains
    • D.S. JERISON AND C.E. KENIG, Boundary behavior of harmonic functions in nontangentially accessible domains, Adv. in Math. 46 (1982), no. 1, 80-147.
    • (1982) Adv. in Math. , vol.46 , Issue.1 , pp. 80-147
    • Jerison, D.S.1    Kenig, C.E.2
  • 15
    • 0000487058 scopus 로고    scopus 로고
    • Harmonic measure on locally flat domains
    • C.E. KENIG AND T. TORO, Harmonic measure on locally flat domains, Duke Math. J. 87 (1997), no. 3, 509-551.
    • (1997) Duke Math. J. , vol.87 , Issue.3 , pp. 509-551
    • Kenig, C.E.1    Toro, T.2
  • 16
    • 0033235413 scopus 로고    scopus 로고
    • Harmonic measures and poisson kernels
    • C.E. KENIG AND T. TORO, Harmonic measures and Poisson Kernels, Ann. of Math. (2) 150 (1999), no. 2, 369-454.
    • (1999) Ann. of Math. (2) , vol.150 , Issue.2 , pp. 369-454
    • Kenig, C.E.1    Toro, T.2
  • 19
    • 84981757198 scopus 로고
    • On the regularity of the solution of a variational inequality
    • H. LEWY AND G. STAMPACCHIA, On the regularity of the solution of a variational inequality, Comm. Pure Appl. Math. 22 (1969) 153-188.
    • (1969) Comm. Pure Appl. Math. , vol.22 , pp. 153-188
    • Lewy, H.1    Stampacchia, G.2
  • 20
    • 51249188913 scopus 로고
    • On the smoothness of superharmonics which solve a minimum problem
    • H. LEWY AND G. STAMPACCHIA, On the smoothness of superharmonics which solve a minimum problem, J. Analyse Math. 23 (1970) 227-236.
    • (1970) J. Analyse Math. , vol.23 , pp. 227-236
    • Lewy, H.1    Stampacchia, G.2
  • 21
    • 51249192844 scopus 로고
    • Solution of the plateau problem for m-dimensional surfaces of varying topological type
    • E.R. REIFENBERG, Solution of the Plateau Problem for m-dimensional surfaces of varying topological type, Acta Math. 104 (1960), 1-92.
    • (1960) Acta Math. , vol.104 , pp. 1-92
    • Reifenberg, E.R.1
  • 22
    • 0016572013 scopus 로고
    • The capacitor problem
    • D.G. SCHAEFFER, The capacitor problem, Indiana Univ. Math. J. 24 (1974/75), no. 12, 1143-1167.
    • (1974) Indiana Univ. Math. J. , vol.24 , Issue.12 , pp. 1143-1167
    • Schaeffer, D.G.1
  • 23
    • 0038862750 scopus 로고
    • A stability theorem for the obstacle problem
    • D.G. SCHAEFFER, A stability theorem for the obstacle problem, Adv. in Math. 17 (1975), no. 1, 34-47.
    • (1975) Adv. in Math. , vol.17 , Issue.1 , pp. 34-47
    • Schaeffer, D.G.1
  • 24
    • 0000708941 scopus 로고
    • Some examples of singularities in a free boundary
    • D.G. SCHAEFFER, Some examples of singularities in a free boundary, Ann. Scuola Norm. Sup. Pisa. 4 (1977), 133-144.
    • (1977) Ann. Scuola Norm. Sup. Pisa , vol.4 , pp. 133-144
    • Schaeffer, D.G.1
  • 25
    • 0031268138 scopus 로고    scopus 로고
    • Perturbation formula for regular free boundaries in elliptic and parabolic obstacle problems
    • S. STOJANOVIC, Perturbation formula for regular free boundaries in elliptic and parabolic obstacle problems, SIAM J. Control Optim. 35 (1997), no. 6, 2086-2100.
    • (1997) SIAM J. Control Optim. , vol.35 , Issue.6 , pp. 2086-2100
    • Stojanovic, S.1
  • 26
    • 84974004393 scopus 로고
    • Geometric conditions and existence of bi-Lipschitz parameterizations
    • T. TORO, Geometric conditions and existence of bi-Lipschitz parameterizations, Duke Math. J. 77 (1995), no. 1, 193-227.
    • (1995) Duke Math. J. , vol.77 , Issue.1 , pp. 193-227
    • Toro, T.1
  • 27
    • 0039455568 scopus 로고    scopus 로고
    • Doubling and flatness: Geometry of measures
    • T. TORO, Doubling and flatness: geometry of measures, Notices Amer. Math. Soc. 44 (1997), no. 9, 1087-1094.
    • (1997) Notices Amer. Math. Soc. , vol.44 , Issue.9 , pp. 1087-1094
    • Toro, T.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.