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Harnack's inequality for degenerate Schrödinger operators
Author:
Cristian E. Gutiérrez
Journal:
Trans. Amer. Math. Soc. 312 (1989), 403-419
MSC:
Primary 35J70; Secondary 35B45, 35J10
MathSciNet review:
948190
Full-text PDF Free Access
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Additional Information
Abstract: We prove a Harnack inequality for nonnegative weak solutions of certain Schrödinger equations of the form  where  is a second order degenerate elliptic operator in divergence form and  is a potential in certain class.
- [1]
F.
Chiarenza, E.
Fabes, and N.
Garofalo, Harnack’s inequality for
Schrödinger operators and the continuity of solutions, Proc. Amer. Math. Soc. 98 (1986), no. 3, 415–425. MR 857933
(88a:35037), http://dx.doi.org/10.1090/S0002-9939-1986-0857933-4
- [2]
R.
R. Coifman and C.
Fefferman, Weighted norm inequalities for maximal functions and
singular integrals, Studia Math. 51 (1974),
241–250. MR 0358205
(50 #10670)
- [3]
Gianni
Dal Maso and Umberto
Mosco, Wiener criteria and energy decay for relaxed Dirichlet
problems, Arch. Rational Mech. Anal. 95 (1986),
no. 4, 345–387. MR 853783
(87m:35021), http://dx.doi.org/10.1007/BF00276841
- [4]
E.
Fabes, D.
Jerison, and C.
Kenig, The Wiener test for degenerate elliptic equations, Ann.
Inst. Fourier (Grenoble) 32 (1982), no. 3, vi,
151–182 (English, with French summary). MR 688024
(84g:35067)
- [5]
Eugene
B. Fabes, Carlos
E. Kenig, and Raul
P. Serapioni, The local regularity of solutions of degenerate
elliptic equations, Comm. Partial Differential Equations
7 (1982), no. 1, 77–116. MR 643158
(84i:35070), http://dx.doi.org/10.1080/03605308208820218
- [6]
E.
B. Fabes and D.
W. Stroock, The 𝐿^{𝑝}-integrability of
Green’s functions and fundamental solutions for elliptic and
parabolic equations, Duke Math. J. 51 (1984),
no. 4, 997–1016. MR 771392
(86g:35057), http://dx.doi.org/10.1215/S0012-7094-84-05145-7
- [7]
David
Kinderlehrer and Guido
Stampacchia, An introduction to variational inequalities and their
applications, Pure and Applied Mathematics, vol. 88, Academic
Press Inc. [Harcourt Brace Jovanovich Publishers], New York, 1980. MR 567696
(81g:49013)
- [8]
Benjamin
Muckenhoupt and Richard
L. Wheeden, Weighted bounded mean oscillation and the Hilbert
transform, Studia Math. 54 (1975/76), no. 3,
221–237. MR 0399741
(53 #3583)
- [9]
Martin
Schechter, Spectra of partial differential operators, 2nd ed.,
North-Holland Series in Applied Mathematics and Mechanics, vol. 14,
North-Holland Publishing Co., Amsterdam, 1986. MR 869254
(88h:35085)
- [1]
- F. Chiarenza, E. Fabes and N. Garofalo, Harnack's inequality for Schrödinger operators and the continuity of solutions, Proc. Amer. Math. Soc. 98 (1986), 415-425. MR 857933 (88a:35037)
- [2]
- R. Coifman and C. Fefferman, Weighted norm inequalities for maximal functions and singular integrals, Studia Math. 51 (1974), 241-250. MR 0358205 (50:10670)
- [3]
- G. Dal Maso and U. Mosco, Wiener criteria and energy decay for relaxed Dirichlet problems, Arch. Rational Mech. Anal. 95 (1986), 347-387. MR 853783 (87m:35021)
- [4]
- E. Fabes. D. Jerison and C. Kenig, The Wiener test for degenerate elliptic equations, Ann. Inst. Fourier (Grenoble) 32 (1982), 151-182. MR 688024 (84g:35067)
- [5]
- E. Fabes, C. Kenig and R. Serapioni, The local regularity of solutions of degenerate elliptic equations, Comm. Partial Differential Equations 7 (1982), 77-116. MR 643158 (84i:35070)
- [6]
- E. Fabes and D. Stroock, The
 -integrability of Green's functions and fundamental solutions for elliptic and parabolic equations, Duke Math. J. 51 (1984), 997-1016. MR 771392 (86g:35057)
- [7]
- D. Kinderlehrer and G. Stamppachia, An introduction to variational inequalities and their applications, Academic Press, New York, 1980. MR 567696 (81g:49013)
- [8]
- B. Muckenhoupt and R. Wheeden, Weighted bounded mean oscillation and the Hilbert transform, Studia Math. 54 (1976), 221-237. MR 0399741 (53:3583)
- [9]
- M. Schechter, Spectra of partial differential operators, North-Holland, Amsterdam, 1971. MR 869254 (88h:35085)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S0002-9947-1989-0948190-6
PII:
S 0002-9947(1989)0948190-6
Article copyright:
© Copyright 1989 American Mathematical Society
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