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Unique continuation for non-negative solutions of quasilinear elliptic equations

Published online by Cambridge University Press:  17 April 2009

Pietro Zamboni
Pietro Zamboni
Affiliation:
Universitá di Catania, Dipartimento di Matematica, viale Andrea Doria 6, 95125 Catania, Italy e-mail: [email protected]
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Abstract

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Dedicated to Filippo Chiarenza

The aim of this note is to prove the unique continuation property for non-negative solutions of the quasilinear elliptic equation

We allow the coefficients to belong to a generalized Kato class.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 64 , Issue 1 , August 2001 , pp. 149 - 156
Copyright
Copyright © Australian Mathematical Society 2001

References

[1]Chanillo, S. and Sawyer, A.E., ‘Unique continuation for Δ + v and the C. Fefferman Phong class’, Trans. Amer. Math. Soc. 318 (1990), 275–300.Google Scholar
[2]Chiarenza, F. and Frasca, M., ‘A remark on a paper by C. Fefferman’, Proc. Amer. Math. Soc. 108 (1990), 407–409.Google Scholar
[3]Chiarenza, F. and Garofalo, N., Unique continuation for non-negative solutions of Schrödinger operators, (Institute for Mathematics and its Applications, Preprint Series No. 122) (University of Minnesota, 1984).Google Scholar
[4]Coifmann, R.R. and Fefferman, C., ‘Weighted norm inequalities for maximal functions and singular integrals’, Studia Math. 51 (1974), 241–250.CrossRefGoogle Scholar
[5]Fabes, E., Garofalo, N. and Lin, F.H., ‘A partial answer to a conjecture of B. Simon concerning unique continuation’, J. Funct. Anal. 88 (1990), 194–210.Google Scholar
[6]Fabes, E., Kenig, C. and Serapioni, R., ‘The local regularity of solutions of degenerate elliptic equations’, comm. Partial Differential Equations 7 (1982), 77–116.Google Scholar
[7]Fefferman, C., ‘The uncertainty principle’, Bull. Amer. Math. Soc. 9 (1983), 129–206.Google Scholar
[8]Cuerva, J. Garcia and de Francia, J.L. Rubio, Weighted norm inequalities and related topics (North-Holland, Amsterdam, 1985).Google Scholar
[9]Giaquinta, M., Multiple integrals in the calculus of variation and linear and nonlinear elliptic systems, Annals of Math. Studies 105 (Princeton University Press, Princeton, NJ, 1983).Google Scholar
[10]schechter, M., Spectra of partial differential operators (second edition), Applied Maths and Mechanics 14 (North Holland Publishing Co., Amsterdam, New York, 1986).Google Scholar
[11]Serrin, J., ‘Local behavior of solutions of quasilinear equations’, Acta Math. 111 (1964), 247–302.Google Scholar
[12]simon, B., ‘Schrödinger semigroups’, Bull. Amer. Math. Soc. 7 (1982), 447–526.CrossRefGoogle Scholar