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Volumn 49, Issue 1, 2005, Pages 159-177

Estimates of Green functions and harmonic measures for elliptic operators with singular drift terms

Author keywords

Drift term; Elliptic operator; Green function; Harmonic measure; Kato class; Poisson kernel

Indexed keywords


EID: 21144436094     PISSN: 02141493     EISSN: None     Source Type: Journal    
DOI: 10.5565/PUBLMAT_49105_07     Document Type: Article
Times cited : (14)

References (28)
  • 1
    • 0032329262 scopus 로고    scopus 로고
    • Norm estimate of Green operator, perturbation of Green function and integrability of superharmonic functions
    • H. AIKAWA, Norm estimate of Green operator, perturbation of Green function and integrability of superharmonic functions, Math. Ann. 312(2) (1998), 289-318.
    • (1998) Math. Ann. , vol.312 , Issue.2 , pp. 289-318
    • Aikawa, H.1
  • 2
    • 84990553776 scopus 로고
    • Brownian motion and Harnack inequality for Schrödinger operators
    • M. AIZENMAN AND B. SIMON, Brownian motion and Harnack inequality for Schrödinger operators, Comm. Pure Appl. Math. 35(2) (1982), 209-273.
    • (1982) Comm. Pure Appl. Math. , vol.35 , Issue.2 , pp. 209-273
    • Aizenman, M.1    Simon, B.2
  • 3
    • 0001577515 scopus 로고
    • Principe de Harnack à la frontiére et théorè me de Fatou pour un opérateur elliptique dans un domaine lipschitzien
    • A. ANCONA, Principe de Harnack à la frontiére et théorème de Fatou pour un opérateur elliptique dans un domaine lipschitzien, Ann. Inst. Fourier (Grenoble) 28(4) (1978), 169-213.
    • (1978) Ann. Inst. Fourier (Grenoble) , vol.28 , Issue.4 , pp. 169-213
    • Ancona, A.1
  • 4
    • 0000605528 scopus 로고
    • Comparaison des mesures harmoniques et des fonctions de Green pour des opérateurs elliptiques sur un domaine lipschitzien
    • A. ANCONA, Comparaison des mesures harmoniques et des fonctions de Green pour des opérateurs elliptiques sur un domaine lipschitzien, C. R. Acad. Sci. Paris Sér. I Math. 294(15) (1982), 505-508.
    • (1982) C. R. Acad. Sci. Paris Sér. I Math. , vol.294 , Issue.15 , pp. 505-508
    • Ancona, A.1
  • 5
    • 0002417396 scopus 로고    scopus 로고
    • First eigenvalues and comparison of Green's functions for elliptic operators on manifolds or domains
    • A. ANCONA, First eigenvalues and comparison of Green's functions for elliptic operators on manifolds or domains, J. Anal. Math. 72 (1997), 45-92.
    • (1997) J. Anal. Math. , vol.72 , pp. 45-92
    • Ancona, A.1
  • 6
    • 0002790745 scopus 로고
    • Continuous solutions of the generalized Schrödinger equation and perturbation of harmonic spaces
    • A. BOUKRICHA, W. HANSEN AND H. HUEBER, Continuous solutions of the generalized Schrödinger equation and perturbation of harmonic spaces, Exposition. Math. 5(2) (1987), 97-135.
    • (1987) Exposition. Math. , vol.5 , Issue.2 , pp. 97-135
    • Boukricha, A.1    Hansen, W.2    Hueber, A.H.3
  • 8
    • 84966211299 scopus 로고
    • Conditional gauge and potential theory for the Schrödinger operator
    • M. CRANSTON, E. FABES AND Z. X. ZHAO, Conditional gauge and potential theory for the Schrödinger operator, Trans. Amer. Math. Soc. 307(1) (1988), 171-194.
    • (1988) Trans. Amer. Math. Soc. , vol.307 , Issue.1 , pp. 171-194
    • Cranston, M.1    Fabes, E.2    Zhao, Z.X.3
  • 9
    • 0039679171 scopus 로고
    • Conditional transformation of drift formula and potential theory for 1/2Δ + &(·)· ∇
    • M. CRANSTON AND Z. X. ZHAO, Conditional transformation of drift formula and potential theory for 1/2Δ + &(·)· ∇, Comm. Math. Phys. 112(4) (1987), 613-625.
    • (1987) Comm. Math. Phys. , vol.112 , Issue.4 , pp. 613-625
    • Cranston, M.1    Zhao, Z.X.2
  • 10
    • 0017727486 scopus 로고
    • Estimates of harmonic measure
    • B. E. J. DAHLBERG, Estimates of harmonic measure, Arch. Rational Mech. Anal. 65(3) (1977), 275-288.
    • (1977) Arch. Rational Mech. Anal. , vol.65 , Issue.3 , pp. 275-288
    • Dahlberg, B.E.J.1
  • 11
    • 0000539082 scopus 로고
    • The Green function for uniformly elliptic equations
    • M. GRÜTER AND K.-O. WIDMAN, The Green function for uniformly elliptic equations, Manuscripta Math. 37(3) (1982), 303-342.
    • (1982) Manuscripta Math. , vol.37 , Issue.3 , pp. 303-342
    • Grüter, M.1    Widman, K.-O.2
  • 12
    • 9744281169 scopus 로고    scopus 로고
    • Normalized solutions of Schrödinger equations with potentially bounded measures
    • W. HANSEN, Normalized solutions of Schrödinger equations with potentially bounded measures, Potential Anal. 21(2) (2004), 99-135.
    • (2004) Potential Anal. , vol.21 , Issue.2 , pp. 99-135
    • Hansen, W.1
  • 14
    • 17744397337 scopus 로고
    • Bibos Publication Universität Bielefeld
    • 1,1-domains, Bibos Publication Universität Bielefeld (1986).
    • (1986) 1,1-domains
    • Hueber, H.1
  • 16
    • 22844456065 scopus 로고    scopus 로고
    • Nonlinear equations and weighted norm inequalities
    • N. J. KALTON AND I. E. VERBITSKY, Nonlinear equations and weighted norm inequalities, Trans. Amer. Math. Soc. 351(9) (1999), 3441-3497.
    • (1999) Trans. Amer. Math. Soc. , vol.351 , Issue.9 , pp. 3441-3497
    • Kalton, N.J.1    Verbitsky, I.E.2
  • 18
    • 0031498748 scopus 로고    scopus 로고
    • Semismall perturbations in the Martin theory for elliptic equations
    • M. MURATA, Semismall perturbations in the Martin theory for elliptic equations, Israel J. Math. 102 (1997), 29-60.
    • (1997) Israel J. Math. , vol.102 , pp. 29-60
    • Murata, M.1
  • 20
    • 0033458245 scopus 로고    scopus 로고
    • Maximum and anti-maximum principles and eigen-functions estimates via perturbation theory of positive solutions of elliptic equations
    • Y. PINCHOVER, Maximum and anti-maximum principles and eigen-functions estimates via perturbation theory of positive solutions of elliptic equations, Math. Ann. 314(3) (1999), 555-590.
    • (1999) Math. Ann. , vol.314 , Issue.3 , pp. 555-590
    • Pinchover, Y.1
  • 21
    • 38249026292 scopus 로고
    • Criticality and ground states for second-order elliptic equations
    • Y. PINCHOVER, Criticality and ground states for second-order elliptic equations, J. Differential Equations 80(2) (1989), 237-250.
    • (1989) J. Differential Equations , vol.80 , Issue.2 , pp. 237-250
    • Pinchover, Y.1
  • 22
    • 14644407737 scopus 로고    scopus 로고
    • 1,1-domains
    • no. 1, Article 22, (electronic).
    • 1,1-domains, JIPAM. J. Inequal. Pure Appl. Math. 4(1) (2003), no. 1, Article 22, 14 pp. (electronic).
    • (2003) JIPAM. J. Inequal. Pure Appl. Math. , vol.4 , Issue.1 , pp. 14
    • Riahi, L.1
  • 23
    • 14644394314 scopus 로고    scopus 로고
    • The 3G-inequality for general Schrödinger operators on Lipschitz domains
    • L. RIAHI, The 3G-inequality for general Schrödinger operators on Lipschitz domains, Manuscripta Math. 116(2) (2005), 211-227.
    • (2005) Manuscripta Math. , vol.116 , Issue.2 , pp. 211-227
    • Riahi, L.1
  • 25
    • 0001602736 scopus 로고    scopus 로고
    • p-spectrum of generalized Schrödinger operators and equivalence of Green's functions
    • p-spectrum of generalized Schrödinger operators and equivalence of Green's functions, Internat. Math. Res. Notices 12 (1997), 573-593.
    • (1997) Internat. Math. Res. Notices , vol.12 , pp. 573-593
    • Semenov, Y.U.A.1
  • 26
    • 0003023464 scopus 로고
    • Inequalities for the Green function and boundary continuity of the gradient of solutions of elliptic differential equations
    • K.-O. WIDMAN, Inequalities for the Green function and boundary continuity of the gradient of solutions of elliptic differential equations, Math. Scand. 21 (1967), 17-37.
    • (1967) Math. Scand. , vol.21 , pp. 17-37
    • Widman, K.-O.1
  • 27
    • 0000916784 scopus 로고
    • Green function for Schrödinger operator and conditioned Feynman-Kac gauge
    • Z. X. ZHAO, Green function for Schrödinger operator and conditioned Feynman-Kac gauge, J. Math. Anal. Appl. 116(2) (1986), 309-334.
    • (1986) J. Math. Anal. Appl. , vol.116 , Issue.2 , pp. 309-334
    • Zhao, Z.X.1
  • 28
    • 0002341788 scopus 로고
    • Subcriticality and gaugeability of the Schrödinger operator
    • Z. X. ZHAO, Subcriticality and gaugeability of the Schrödinger operator, Trans. Amer. Math. Soc. 334(1) (1992), 75-96.
    • (1992) Trans. Amer. Math. Soc. , vol.334 , Issue.1 , pp. 75-96
    • Zhao, Z.X.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.