메뉴 건너뛰기




Volumn 9, Issue 3, 1998, Pages 201-216

Irregular Solutions of Linear Degenerate Elliptic Equations

Author keywords

De Giorgi Nash theorem; Linear degenerate elliptic equations; Regular solutions; Weights

Indexed keywords


EID: 0032262792     PISSN: 09262601     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1008684127989     Document Type: Article
Times cited : (31)

References (28)
  • 1
    • 0039759936 scopus 로고
    • Traces of potentials arising from translation invariant operators
    • Adams, D. R.: 'Traces of potentials arising from translation invariant operators', Ann. Scuola Norm. Sup. Pisa (III) 25 (1971), 203-217.
    • (1971) Ann. Scuola Norm. Sup. Pisa (III) , vol.25 , pp. 203-217
    • Adams, D.R.1
  • 2
    • 0000376647 scopus 로고
    • Principe de maximum, inégalité de Harnack et unicité du problème de Cauchy pour les opérateurs elliptiques dégénérés
    • Bony, J.-M.: 'Principe de maximum, inégalité de Harnack et unicité du problème de Cauchy pour les opérateurs elliptiques dégénérés', Ann. Inst. Fourier, Grenoble 19 (1969), 277-304.
    • (1969) Ann. Inst. Fourier, Grenoble , vol.19 , pp. 277-304
    • Bony, J.-M.1
  • 3
    • 0001241250 scopus 로고
    • An embedding theorem and Harnack inequality for nonlinear subelliptic equations
    • Capogna, L., Danielli, D. and Garofalo, N.: 'An embedding theorem and Harnack inequality for nonlinear subelliptic equations', Comm. Partial Diff. Equations 18 (1993), 1765-1794.
    • (1993) Comm. Partial Diff. Equations , vol.18 , pp. 1765-1794
    • Capogna, L.1    Danielli, D.2    Garofalo, N.3
  • 4
    • 0042735238 scopus 로고
    • De Giorgi-Moser theorem for a class of degenerate non uniformly elliptic equations
    • Chiarenza, F., Rustichini, A. and Serapioni, R.: 'De Giorgi-Moser theorem for a class of degenerate non uniformly elliptic equations', Comm. Partial Diff. Equations 14 (5) (1989), 635-662.
    • (1989) Comm. Partial Diff. Equations , vol.14 , Issue.5 , pp. 635-662
    • Chiarenza, F.1    Rustichini, A.2    Serapioni, R.3
  • 5
    • 0001763939 scopus 로고
    • Harnack's inequality and mean value for the solutions of degenerate elliptic equations
    • Chanillo, S. and Wheeden, R. L.: 'Harnack's inequality and mean value for the solutions of degenerate elliptic equations', Comm. Partial Diff. Equations 11 (1986), 1111-1134.
    • (1986) Comm. Partial Diff. Equations , vol.11 , pp. 1111-1134
    • Chanillo, S.1    Wheeden, R.L.2
  • 6
    • 0002412307 scopus 로고
    • Sulla differenziabilità e l'analiticità delle estremali degli integrali multipli regolari
    • DeGiorgi, E.: 'Sulla differenziabilità e l'analiticità delle estremali degli integrali multipli regolari', Mem. Accad. Sci. Torino Cl. Sci. Fis. Mat. Natur. 3 (1957), 25-43.
    • (1957) Mem. Accad. Sci. Torino Cl. Sci. Fis. Mat. Natur. , vol.3 , pp. 25-43
    • DeGiorgi, E.1
  • 8
    • 0012375319 scopus 로고
    • Two-weight Sobolev-Poincaré inequalities and Harnack inequality for a class of degenerate elliptic operators
    • Franchi, B., Gutierrez, C. E. and Wheeden, R. L.: 'Two-weight Sobolev-Poincaré inequalities and Harnack inequality for a class of degenerate elliptic operators', Atti Acad. Naz. Lincei, Cl. Sci. Fis. Mat. Nat. 5 (1994), 167-175.
    • (1994) Atti Acad. Naz. Lincei, Cl. Sci. Fis. Mat. Nat. , vol.5 , pp. 167-175
    • Franchi, B.1    Gutierrez, C.E.2    Wheeden, R.L.3
  • 9
    • 0001077590 scopus 로고
    • Weighted Poincaré and Sobolev inequalities for Grushin type operators
    • Franchi, B., Gutierrez, C. E. and Wheeden, R. L.: 'Weighted Poincaré and Sobolev inequalities for Grushin type operators', Comm. Partial Diff. Equations 19 (1994), 523-604.
    • (1994) Comm. Partial Diff. Equations , vol.19 , pp. 523-604
    • Franchi, B.1    Gutierrez, C.E.2    Wheeden, R.L.3
  • 10
    • 0003035995 scopus 로고
    • The local regularity of solutions of degenerate elliptic equations
    • Fabes, E. B., Kenig, C. E. and Serapioni, R.: 'The local regularity of solutions of degenerate elliptic equations', Comm. Partial Diff. Equations 7 (1982), 77-116.
    • (1982) Comm. Partial Diff. Equations , vol.7 , pp. 77-116
    • Fabes, E.B.1    Kenig, C.E.2    Serapioni, R.3
  • 11
    • 0000541936 scopus 로고
    • Hölder regularity theorem for a class of linear non uniformly elliptic operators with measurable coefficients
    • Franchi, B. and Lanconelli, E.: 'Hölder regularity theorem for a class of linear non uniformly elliptic operators with measurable coefficients', Ann. Scuola Norm. Sup. Pisa (IV), 10, (1983), 523-541.
    • (1983) Ann. Scuola Norm. Sup. Pisa (IV) , vol.10 , pp. 523-541
    • Franchi, B.1    Lanconelli, E.2
  • 13
    • 0001740045 scopus 로고
    • Pointwise estimates for strongly degenerate elliptic operators: A geometrical approach
    • Franchi, B. and Serapioni, R.: 'Pointwise estimates for strongly degenerate elliptic operators: a geometrical approach', Ann. Scuola Norm. Sup. Pisa (IV), 14 (1987), 527-568.
    • (1987) Ann. Scuola Norm. Sup. Pisa (IV) , vol.14 , pp. 527-568
    • Franchi, B.1    Serapioni, R.2
  • 15
    • 84972555264 scopus 로고
    • The Poincaré inequality for vector fields satisfying Hórmander's condition
    • Jerison, D.: 'The Poincaré inequality for vector fields satisfying Hórmander's condition', Duke Math. J. 53 (1986), 503-523.
    • (1986) Duke Math. J. , vol.53 , pp. 503-523
    • Jerison, D.1
  • 16
    • 0001207007 scopus 로고
    • Weighted Poincaré and Sobolev inequalities for vector fields satisfying Hörmander's condition and applications
    • Lu, G.: 'Weighted Poincaré and Sobolev inequalities for vector fields satisfying Hörmander's condition and applications', Revista Math. Iberoamericana 8 (1992), 367-439.
    • (1992) Revista Math. Iberoamericana , vol.8 , pp. 367-439
    • Lu, G.1
  • 18
    • 0003796632 scopus 로고
    • Springer-Verlag, Berlin-Heidelberg-New York
    • Maz'ja, V. G.: Sobolev Spaces, Springer-Verlag, Berlin-Heidelberg-New York, 1980.
    • (1980) Sobolev Spaces
    • Maz'ja, V.G.1
  • 19
    • 84980088516 scopus 로고
    • A new proof of de Giorgi's theorem concerning the regularity problem for elliptic differential equations
    • Moser, J.: 'A new proof of De Giorgi's theorem concerning the regularity problem for elliptic differential equations', Comm. Pure Appl. Math. 13 (1960), 457-468.
    • (1960) Comm. Pure Appl. Math. , vol.13 , pp. 457-468
    • Moser, J.1
  • 20
    • 84980080977 scopus 로고
    • On Harnack's theorem for elliptic differential equations
    • Moser, J.: 'On Harnack's theorem for elliptic differential equations', Comm. Pure Appl. Math. 14 (1961), 577-591.
    • (1961) Comm. Pure Appl. Math. , vol.14 , pp. 577-591
    • Moser, J.1
  • 21
    • 0002465923 scopus 로고
    • Boundary value problems for some degenerateelliptic operators
    • Murthy, M. K. V. and Stampacchia. G.: 'Boundary value problems for some degenerateelliptic operators', Ann. Mat. Pura Appl. 80 (1968), 1-122.
    • (1968) Ann. Mat. Pura Appl. , vol.80 , pp. 1-122
    • Murthy, M.K.V.1    Stampacchia, G.2
  • 22
    • 0001680091 scopus 로고
    • Continuity of solutions of parabolic and elliptic equations
    • Nash, J.: 'Continuity of solutions of parabolic and elliptic equations', Amer. J. Math. 80 (1958), 931-954.
    • (1958) Amer. J. Math. , vol.80 , pp. 931-954
    • Nash, J.1
  • 23
    • 0000281633 scopus 로고
    • Pathological solutions of elliptic differential equations
    • Serrin, J.: 'Pathological solutions of elliptic differential equations', Ann. Sc. Norm. Sup. Pisa, Cl.Sc.(4) 17-18 (1964), 385-387.
    • (1964) Ann. Sc. Norm. Sup. Pisa, Cl.Sc.(4) , vol.17-18 , pp. 385-387
    • Serrin, J.1
  • 24
    • 0042234248 scopus 로고
    • A counterexample to the weighted Poincaré inequality
    • Serra Cassano, F.: 'A counterexample to the weighted Poincaré inequality', Rend. Sem. Mat. Univ. Pol. Torino 51 (1993), 62-67.
    • (1993) Rend. Sem. Mat. Univ. Pol. Torino , vol.51 , pp. 62-67
    • Serra Cassano, F.1
  • 25
    • 0043236467 scopus 로고    scopus 로고
    • On the local boundedness of certain solutions for a class of degenerate elliptic equations
    • to appear
    • Serra Cassano, F.: On the local boundedness of certain solutions for a class of degenerate elliptic equations, Boll. Un. Mat. Ital., to appear.
    • Boll. Un. Mat. Ital.
    • Serra Cassano, F.1
  • 26
    • 0000444043 scopus 로고
    • Weighted inequalities for fractional integrals on Euclidean and homogeneus spaces
    • Sawyer, E. and Wheeden, R. L.: 'Weighted inequalities for fractional integrals on Euclidean and homogeneus spaces', Amer. J. Math. 114 (1992), 813-874.
    • (1992) Amer. J. Math. , vol.114 , pp. 813-874
    • Sawyer, E.1    Wheeden, R.L.2
  • 27
    • 34250467463 scopus 로고
    • On the regularity of generalized solutions of linear non uniformly elliptic equations
    • Trudinger, N. S.: 'On the regularity of generalized solutions of linear non uniformly elliptic equations', Arch. Rat. Mech. Anal. 42 (1971), 51-62.
    • (1971) Arch. Rat. Mech. Anal. , vol.42 , pp. 51-62
    • Trudinger, N.S.1
  • 28
    • 0006027422 scopus 로고
    • Linear Elliptic Operators with Measurable Coefficients
    • Trudinger, N. S.: 'Linear Elliptic Operators with Measurable Coefficients', Ann. Scuola Norm. Sup. Pisa (3) (III), 27 (1973), 265-308.
    • (1973) Ann. Scuola Norm. Sup. Pisa (3) (III) , vol.27 , pp. 265-308
    • Trudinger, N.S.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.