The strong maximum principle for Schrödinger operators on fractals

• Autorzy: Ionescu Marius V. , Okoudjou Kasso A. , Rogers Luke G.

Identyfikatory

DOI

10.1515/dema-2019-0034

• Języki publikacji: EN

Abstrakty

EN

We prove a strong maximum principle for Schrödinger operators defined on a class of postcritically finite fractal sets and their blowups without boundary. Our primary interest is in weaker regularity conditions than have previously appeared in the literature; in particular we permit both the fractal Laplacian and the potential to be Radon measures on the fractal. As a consequence of our results, we establish a Harnack inequality for solutions of these operators.

Słowa kluczowe

EN

analysis on fractals; Harnack’s inequality; maximum principles Sierpiński gasket; Schrödinger operators

PL

analiza fraktalna; nierówność Harnacka; uszczelka Sierpińskiego; operatory Schrödingera

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2019
• Tom: Vol. 52, nr 1
• Strony: 404--409
• Opis fizyczny: Bibliogr. 10 poz.

Twórcy

autor

Ionescu Marius V.

• Department of Mathematics, United States Naval Academy, Annapolis, MD, 21402-5002, USA

autor

Okoudjou Kasso A.

• Department of Mathematics and Norbert Wiener Center, University of Maryland,College Park, MD 20742, USA

autor

Rogers Luke G.

• Department of Mathematics, University of Connecticut, Storrs, CT 06269-1009, USA

Bibliografia

• [1] Strichartz R. S., Some properties of Laplacians on fractals, J. Funct. Anal., 1999, 164(2), 181-208
• [2] Kigami K., Analysis on fractals, Cambridge Tracts in Mathematics, vol. 143, Cambridge University Press, Cambridge, 2001
• [3] Strichartz R. S., Differential equations on fractals, A tutorial, Princeton University Press, Princeton, NJ, 2006
• [4] Kigami K., Harmonic calculus on p.c.f. self-similar sets, Trans. Amer. Math. Soc., 1993, 335(2), 721-755
• [5] Fukushima M., Oshima Y., Takeda M., Dirichlet forms and symmetric Markov processes, extended ed., de Gruyter Studies in Mathematics, vol. 19, Walter de Gruyter & Co., Berlin, 2011
• [6] Strichartz R. S., Usher M., Splines on fractals, Math. Proc. Cambridge Philos. Soc., 2000, 129(2), 331-360
• [7] Kigami K., Harmonic analysis for resistance forms, J. Funct. Anal., 2003, 204(2), 399-444
• [8] Strichartz R. S., Fractals in the large, Canad. J. Math., 1998, 50(3), 638-657
• [9] Rogers L. G., Estimates for the resolvent kernel of the Laplacian on p.c.f. self-similar fractals and blowups, Trans. Amer. Math. Soc., 2012, 364(3), 1633-1685
• [10] Gilbarg D., Trudinger N. S., Elliptic partial differential equations of second order, Classics in Mathematics, Springer-Verlag, Berlin, 2001, Reprint of the 1998 edition

Uwagi

PL

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).