Evans Harrell

Professor School of Mathematics&Associate Dean College of SciencesGeorgia Institute of TechnologyAtlanta GA 30332-0365 email:h a r r e l l (at) math.gatech.eduPhone: (404) 894 3300

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Some publications

1. Spectra and Schrödinger operators
   1. On semiclassical and universal inequalities for eigenvalues of quantum graphs, Rev. Math. Phys. 22(2010)305-329 (with S. Demirel), available as arXiv:/0911.1896
   2. Trace identities for commutators, with applications to the distribution of eigenvalues , to appear in Trans. Amer. Math. Soc. (with J. Stubbe, available as arXiv:/0903.0563.
   3. Universal bounds and semiclassical estimates for eigenvalues of abstract Schrödinger operators, with J. Stubbe, to appear in SIAM J. Math. Analysis, available as arXiv:0808.1133.
   4. Eigenvalue inequalities for Klein-Gordon operators, with S. Yildirim Yolcu, J. Funct. Analysis 256 (2009)3977-3995, also available as arXiv:0810.0059.
   5. On Riesz means of eigenvalues, with L. Hermi, preprint, 2007, available as arXiv:0712.4088v1.
   6. Differential inequalities for Riesz means and Weyl-type bounds for eigenvalues, with L. Hermi, J. Funct. Analysis 254 (2008)3173-3191, also available as arXiv:0705.3673.
   7. Perturbation Theory and Atomic Resonances since Schrödinger's Time, a review for the Simon Fest, Caltech, 2006, published as pp. 227-248 in: P. Deift, F. Gesztesy. P. Perry, and W. Schlag, eds., Spectral Theory and Mathematical Physics: A Festschrift in Honor of Barry Simon's 60th Birthday, Proceedings of Symposia in Pure Mathematics 76.1. Providence: American Mathematical Society, 2007.
   8. On the fundamental eigenvalue ratio of the p-Laplacian, with J. Fleckinger and F. de Thélin, Bulletin des Sciences Mathématiques 131(2007)613-619.
   9. Geometric lower bounds for the spectrum, Journal of Computational and Applied Mathematics 194(2006)26-35. The 1907 article by Boggio referred to in this article can be viewed here.
   10. Commutators, eigenvalue gaps, and mean curvature in the theory of Schrödinger operators (preprint version), Commun. Part. Diff. Eq. 32(2007)401-413.
   11. On the placement of an obstacle or well so as to optimize the fundamental eigenvalue, with P. Kröger and K. Kurata, SIAM J. Math. Analysis 33(2001)240-259.
   12. Optimal eigenvalues for some Laplacians and Schrödinger operators depending on curvature, with P. Exner and M. Loss, pp. 47-58 in J. Dittrich, P. Exner, and M. Tater, eds., Mathematical Results in Quantum Mechanics. Basel: Birkhäuser, 1999. This is the text of my plenary lecture at the meeting QMath7, June 1998 (dvi file or pdf file).
   13. On the Laplace operator penalized by mean curvature, with M. Loss. Commun. Math. Phys. 195(1998)643-650 (TeX file)
   14. On trace identities and universal eigenvalue estimates for some partial differential operators, with J. Stubbe, Trans. Amer. Math. Soc., 349(1997)1797-1809. (dvi file or talk slides)
   Also see Inequalities for means of chords, with application to isoperimetric problems and Universal inequalities for the eigenvalues of Laplace and Schrödinger operators on submanifolds listed under "geometry" and On semiclassical and universal inequalities for eigenvalues of quantum graphs listed under "nanotechnology".
2. Geometry
   1. On the maximization of a class of functionals on convex regions, and the characterization of the farthest convex set, to appear in Mathematika (with A. Henrot), available as arXiv:/0905.1464v1.
   2. On the critical exponent in an isoperimetric inequality for chords, Physics Letters A 365(2007)1-6, with P. Exner and M. Fraas.
   3. Universal inequalities for the eigenvalues of Laplace and Schrödinger operators on submanifolds, with A. El Soufi and S. Ilias, to appear in Trans. Amer. Math. Soc.
   4. Inequalities for means of chords, with application to isoperimetric problems, with P. Exner and M. Loss, Letters in Mathematical Physics 75(2006)225-233.
   5. A direct proof of a theorem of Blaschke and Lebesgue, Journal of Geometric Analysis 12(2002)81-88. (tex preprint, a figure in which is a separate eps file, or pdf preprint).
3. Nonlinear partial differential equations
   1. Asymptotics for solutions of some nonlinear partial differential equations on unbounded domains, with J. Fleckinger and F. de Thélin, Electronic J. Diff. Eqns. 2001((2001) No. 77, pp. 1-14. ( Go there.)
   2. Boundary behavior and L^q estimates for solutions of equations containing the p-Laplacian, with J. Fleckinger and F. de Thélin, Electronic J. Diff. Eqns. 1999(1999) No. 38, pp. 1-19. ( Go there.)
   Also see Geometric lower bounds for the spectrum of elliptic PDEs and On the fundamental eigenvalue ratio of the p-Laplacian, listed under "spectra"..
4. Nanotechnology
   1. On semiclassical and universal inequalities for eigenvalues of quantum graphs, with S. Demirel, available as arXiv:/0911.1896
   2. A Physical Short-Channel Threshold Voltage Model for Undoped Symmetric Double-Gate MOSFET's, IEEE Transactions on Electron Devices 50(2003)1631-1637 (with Q. Chen and J.D. Meindl), 2003. Go there
   3. Double Jeopardy: Defending MOSFET Technology at the Nanoscale Court, IEEE Circuits and Devices Magazine 19(1) (2003)28-34 (with Q. Chen, K. A. Bowman, and J.D. Meindl). Go there
5. Miscellany
   1. How to Win a Fellowship for Graduate Study in Mathematics, Math Horizons 12 (2004) 15.
   2. Book review of Visual Quantum Mechanics, by Bernd Thaller, SIAM Review 39 (2)(2001)385-388.
   3. My WWW textbook with James Herod, Linear Methods of Applied Mathematics: Orthogonal series, boundary-value problems, and integral operators (which can be used in Math 4582 and 4348 at Georgia Tech).
6. Some on-line lectures
   1. Sharp geometric bounds for eigenvalues of Schrödinger operators, slides from the talk given at the September, 2006, meeting on Operator Theory in Quantum Physics (OTQP) (PDF).
   2. Perturbation theory and atomic resonances since Schrödinger's time, slides from the talk given at the March, 2006 Simon Fest (PDF)
   3. Isoperimetric problems arising in the physics of thin structures , a seminar given at Mississippi State and at Tucson, 2006. ( pdf.)
   4. The extreme sport of eigenvalue hunting , a lecture for graduate students. (Powerpoint)
   5. Commutators, eigenvalue gaps, and quantum mechanics on surfaces (Powerpoint or PDF). Colloquium given in Tucson and Tours, 2004.
   6. Universal spectral bounds for Schrödinger operators on surfaces (Powerpoint or PDF). QMath9, Giens, France, September, 2004.
   7. Some geometric bounds on eigenvalues of elliptic PDEs (Powerpoint or PDF), Cardiff, Wales, July, 2004.
   8. The lightest coins and the lightest rollng bearings. Colloquium on convex bodies of constant width.
   9. Gap estimates for Schrödinger operators depending on curvature, UAB, Birmingham, Alabama, 2002. (Format: PDF)
   10. A direct proof of a theorem of Blaschke and Lebesgue, seminar, 2002.

A more complete publication list is available here.

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