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Volumn 150, Issue 1, 1999, Pages 313-327

Doubling properties for second order parabolic equations

(2)  Safonov, Mikhail V a   Yuan, Yu a  

a NONE

Author keywords

Doubling property; Fatou theorem; L caloric measure

Indexed keywords


EID: 0033244832     PISSN: 0003486X     EISSN: None     Source Type: Journal    
DOI: 10.2307/121104     Document Type: Article
Times cited : (32)

References (22)
  • 1
    • 0030536801 scopus 로고    scopus 로고
    • Caloric functions in Lipschitz domains and the regularity of solutions to phase transition problems
    • I. ATHANASOPOULOS, L. A. CAFFARELLI and S. SALSA, Caloric functions in Lipschitz domains and the regularity of solutions to phase transition problems, Ann. of Math. 143 (1996), 413-434.
    • (1996) Ann. of Math. , vol.143 , pp. 413-434
    • Athanasopoulos, I.1    Caffarelli, L.A.2    Salsa, S.3
  • 2
    • 0000377165 scopus 로고
    • Non-negative solutions of linear parabolic equations
    • D. G. ARONSON, Non-negative solutions of linear parabolic equations, Ann. Scuola Norm. Sup. Pisa 22 (1968), 607-694.
    • (1968) Ann. Scuola Norm. Sup. Pisa , vol.22 , pp. 607-694
    • Aronson, D.G.1
  • 4
    • 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), 621-640.
    • (1981) Indiana Univ. Math. J. , vol.30 , pp. 621-640
    • Caffarelli, L.A.1    Fabes, E.B.2    Mortola, S.3    Salsa, S.4
  • 6
    • 84972575662 scopus 로고
    • A backward Harnack inequality and fatou theorem for nonnegative solutions of parabolic equations
    • E. B. FABES, N. GAROFALO and S. SALSA, A backward Harnack inequality and Fatou theorem for nonnegative solutions of parabolic equations, Illinois J. of Math. 30 (1986), 536-565.
    • (1986) Illinois J. of Math. , vol.30 , pp. 536-565
    • Fabes, E.B.1    Garofalo, N.2    Salsa, S.3
  • 7
    • 84972568429 scopus 로고
    • Examples of singular parabolic measures and singular transition probability densities
    • E. B. FABES and C. E. KENIG, Examples of singular parabolic measures and singular transition probability densities, Duke Math. J. 48 (1981), 845-856.
    • (1981) Duke Math. J. , vol.48 , pp. 845-856
    • Fabes, E.B.1    Kenig, C.E.2
  • 9
    • 22844456928 scopus 로고    scopus 로고
    • Behavior near the boundary of positive solutions of second order parabolic equations. II
    • to appear in
    • E. B. FABES, M. V. SAFONOV and Y. YUAN, Behavior near the boundary of positive solutions of second order parabolic equations. II, to appear in Trans. A.M.S., 1999.
    • (1999) Trans. A.M.S.
    • Fabes, E.B.1    Safonov, M.V.2    Yuan, Y.3
  • 10
    • 33646917618 scopus 로고
    • A new proof of Moser's parabolic Harnack inequality using the old ideas of Nash
    • E. B. FABES and D. W. STROOCK, A new proof of Moser's parabolic Harnack inequality using the old ideas of Nash, Arch. Rational Mech. Anal. 96 (1986), 327-338.
    • (1986) Arch. Rational Mech. Anal. , vol.96 , pp. 327-338
    • Fabes, E.B.1    Stroock, D.W.2
  • 11
    • 34250285233 scopus 로고
    • Second order parabolic equations in nonvariational form: Boundary harnack principle and comparison theorems for nonnegative solutions
    • N. GAROFALO, Second order parabolic equations in nonvariational form: boundary Harnack principle and comparison theorems for nonnegative solutions, Ann. Mat. Pura Appl. 138 (1984), 267-296.
    • (1984) Ann. Mat. Pura Appl. , vol.138 , pp. 267-296
    • Garofalo, N.1
  • 13
    • 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), 80-147.
    • (1982) Adv. in Math. , vol.46 , pp. 80-147
    • Jerison, D.S.1    Kenig, C.E.2
  • 14
    • 0003307061 scopus 로고
    • Harmonic analysis techniques for second order elliptic boundary value problems
    • C. E. KENIG, Harmonic Analysis Techniques for Second Order Elliptic Boundary Value Problems, CBMS Regional Conference Series in Mathematics 83, 1994.
    • (1994) CBMS Regional Conference Series in Mathematics , vol.83
    • Kenig, C.E.1
  • 16
    • 0002851231 scopus 로고    scopus 로고
    • A property of the solutions of parabolic equations with measurable coefficients
    • N. V. KRYLOV and M. V. SAFONOV, A property of the solutions of parabolic equations with measurable coefficients, Izvestia Akad. Nauk SSSR, Ser. Matem. 44 English transl. in Math. USSR Izvestija 16 (1981), 151-164.
    • Izvestia Akad. Nauk SSSR, Ser. Matem. , vol.44
    • Krylov, N.V.1    Safonov, M.V.2
  • 17
    • 0002851231 scopus 로고    scopus 로고
    • N. V. KRYLOV and M. V. SAFONOV, A property of the solutions of parabolic equations with measurable coefficients, Izvestia Akad. Nauk SSSR, Ser. Matem. 44 English transl. in Math. USSR Izvestija 16 (1981), 151-164.
    • (1981) Math. Ussr Izvestija , vol.16 , pp. 151-164
  • 19
    • 0003744099 scopus 로고
    • Providence, RI
    • O. A. LADYZHENSKAYA, V. A. SOLONNIKOV and N. N. URAL'TSEVA, Linear and Auasi-Linear Euations of Parabolic Type, Nauka, Moscow, 1967 in Russian; English transl.: Amer. Math. Soc., Providence, RI, 1967.
    • (1967) Amer. Math. Soc.
  • 20
    • 84980078895 scopus 로고
    • A Harnack inequality for parabolic differential equations
    • correction in op. cit. 20 (1967) 231-236
    • J. MOSER, A Harnack inequality for parabolic differential equations, Comm. Pure and Appl. Math. 17 (1964) 101-134; correction in op. cit. 20 (1967) 231-236.
    • (1964) Comm. Pure and Appl. Math. , vol.17 , pp. 101-134
    • Moser, J.1
  • 21
    • 84980178619 scopus 로고
    • On a pointwise estimate for parabolic differential equations
    • _, On a pointwise estimate for parabolic differential equations, Comm. Pure and Appl. Math. 24 (1971) 727-740.
    • (1971) Comm. Pure and Appl. Math. , vol.24 , pp. 727-740


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.