Harnack’s inequality for degenerate Schrödinger operators
HTML articles powered by AMS MathViewer
- by Cristian E. Gutiérrez PDF
- Trans. Amer. Math. Soc. 312 (1989), 403-419 Request permission
Abstract:
We prove a Harnack inequality for nonnegative weak solutions of certain Schrödinger equations of the form $Lu - Vu = 0$ where $L$ is a second order degenerate elliptic operator in divergence form and $V$ is a potential in certain class.References
- 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, DOI 10.1090/S0002-9939-1986-0857933-4
- R. R. Coifman and C. Fefferman, Weighted norm inequalities for maximal functions and singular integrals, Studia Math. 51 (1974), 241–250. MR 358205, DOI 10.4064/sm-51-3-241-250
- 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, DOI 10.1007/BF00276841
- 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, DOI 10.5802/aif.883
- 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, DOI 10.1080/03605308208820218
- 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, DOI 10.1215/S0012-7094-84-05145-7
- 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-London, 1980. MR 567696
- Benjamin Muckenhoupt and Richard L. Wheeden, Weighted bounded mean oscillation and the Hilbert transform, Studia Math. 54 (1975/76), no. 3, 221–237. MR 399741, DOI 10.4064/sm-54-3-221-237
- 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
Additional Information
- © Copyright 1989 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 312 (1989), 403-419
- MSC: Primary 35J70; Secondary 35B45, 35J10
- DOI: https://doi.org/10.1090/S0002-9947-1989-0948190-6
- MathSciNet review: 948190