CURRICULUM VITAE YEKATERINA EPSHTEYN Summer 2021
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How a Minimal Surface Leaves an Obstacle
HOW A MINIMAL SURFACE LEAVES AN OBSTACLE BY DAVID KINDERLEHRER University of Minnesota, Minneapolis, MN 55455, USA (1) This paper is an investigation of the curve of separation determined by the solution to a variational inequality for minimal surfaces. A strictly convex domain ~ in the z = x 1 +ix~ plane is given together with a smooth function ~p which assumes a positive maxi- mum in ~ and is negative on ~, the boundary of ~. Let u denote the Lipschitz function which minimizes area among all Lipschitz functions in ~ constrained to lie above ~p in and to vanish on a~. For such u there is a coincidence set I c ~ consisting of those points z where u(z)=yJ(z). Let us call F={(xl, x~, xa): xa=u(z)=y~(z), zE~I} the "curve" of se- paration. The object of this paper is to show that F is analytic, as a function of its arc length parameter, provided that y; is strictly concave and analytic. The study of the coincidence set of the solution to a variational inequality and its curve of separation was originated, together with the study of the regularity of the solu- tion, by H. Lewy and G. Stampacchia ([11)]. They obtained, essentially, the result pre- sented here for the variational inequality derived from the Dirichlet Integral. The topo- logical conclusion that r is a Jordan curve was reached under the assumption that yJ E C2(~) be strictly concave, a conclusion valid for a wide variety of cases, in particular the problem treated in this paper ([6]). Our demonstration reties on the resolution of a system of differential equations and the utilization of the solution to extend analytically a conformal representation of the minimal surface which is the graph of u in the subset of ~ where u(z)>~(z). -
Society Reports USNC/TAM
Appendix J 2008 Society Reports USNC/TAM Table of Contents J.1 AAM: Ravi-Chandar.............................................................................................. 1 J.2 AIAA: Chen............................................................................................................. 2 J.3 AIChE: Higdon ....................................................................................................... 3 J.4 AMS: Kinderlehrer................................................................................................. 5 J.5 APS: Foss................................................................................................................. 5 J.6 ASA: Norris............................................................................................................. 6 J.7 ASCE: Iwan............................................................................................................. 7 J.8 ASME: Kyriakides.................................................................................................. 8 J.9 ASTM: Chona ......................................................................................................... 9 J.10 SEM: Shukla ....................................................................................................... 11 J.11 SES: Jasiuk.......................................................................................................... 13 J.12 SIAM: Healey...................................................................................................... 14 J.13 SNAME: Karr.................................................................................................... -
Curriculum Vitae
Umberto Mosco WPI Harold J. Gay Professor of Mathematics May 18, 2021 Department of Mathematical Sciences Phone: (508) 831-5074, Worcester Polytechnic Institute Fax: (508) 831-5824, Worcester, MA 01609 Email: [email protected] Curriculum Vitae Current position: Harold J. Gay Professor of Mathematics, Worcester Polytechnic Institute, Worcester MA, U.S.A. Languages: English, French, German, Italian (mother language) Specialization: Applied Mathematics Research Interests:: Fractal and Partial Differential Equations, Homog- enization, Finite Elements Methods, Stochastic Optimal Control, Variational Inequalities, Potential Theory, Convex Analysis, Functional Convergence. Twelve Most Relevant Research Articles 1. Time, Space, Similarity. Chapter of the book "New Trends in Differential Equations, Control Theory and Optimization, pp. 261-276, WSPC-World Scientific Publishing Company, Hackenseck, NJ, 2016. 2. Layered fractal fibers and potentials (with M.A.Vivaldi). J. Math. Pures Appl. 103 (2015) pp. 1198-1227. (Received 10.21.2013, Available online 11.4.2014). 3. Vanishing viscosity for fractal sets (with M.A.Vivaldi). Discrete and Con- tinuous Dynamical Systems - Special Volume dedicated to Louis Niren- berg, 28, N. 3, (2010) pp. 1207-1235. 4. Fractal reinforcement of elastic membranes (with M.A.Vivaldi). Arch. Rational Mech. Anal. 194, (2009) pp. 49-74. 5. Gauged Sobolev Inequalities. Applicable Analysis, 86, no. 3 (2007), 367- 402. 6. Invariant field metrics and dynamic scaling on fractals. Phys. Rev. Let- ters, 79, no. 21, Nov. (1997), pp. 4067-4070. 7. Variational fractals. Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 25 (1997) No. 3-4, pp. 683-712. 8. A Saint-Venant type principle for Dirichlet forms on discontinuous media (with M. -
Notices of the American Mathematical Society Is Everything Other Than Meetings and Publications
OTICES OF THE AMERICAN MATHEMATICAL SOCIETY ICM-90 Second Announcement page 188 Manhattan Meeting (March 16-17) page 148 Fayetteville Meeting (March 23-24) page 162 990 Cole Prize page 118 1990 Award for Distinguished Public Service page 120 FEBRUARY 1990, VOLUME 37, NUMBER 2 Providence, Rhode Island, USA ISSN 0002-9920 Calendar of AMS Meetings and Conferences This calendar lists all meetings which have been approved prior to Mathematical Society in the issue corresponding to that of the Notices the date this issue of Notices was sent to the press. The summer which contains the program of the meeting, insofar as is possible. and annual meetings are joint meetings of the Mathematical Associ Abstracts should be submitted on special forms which are available in ation of America and the American Mathematical Society. The meet many departments of mathematics and from the headquarters office ing dates which fall rather far in the future are subject to change; this of the Society. Abstracts of papers to be presented at the meeting is particularly true of meetings to which no numbers have been as must be received at the headquarters of the Society in Providence, signed. Programs of the meetings will appear in the issues indicated Rhode Island, on or before the deadline given below for the meet below. First and supplementary announcements of the meetings will ing. Note that the deadline for abstracts for consideration for pre have appeared in earlier issues. sentation at special sessions is usually three weeks earlier than that Abstracts of papers presented at a meeting of the Society are pub specified below. -
Hans Lewy Papers
http://oac.cdlib.org/findaid/ark:/13030/kt8f59q33c No online items Guide to the Hans Lewy Papers Processed by Ania Laszcz. The Bancroft Library. University of California, Berkeley Berkeley, California, 94720-6000 Phone: (510) 642-6481 Fax: (510) 642-7589 Email: [email protected] URL: http://bancroft.berkeley.edu © 2003 The Regents of the University of California. All rights reserved. Guide to the Hans Lewy Papers BANC MSS 91/147 cz 1 Guide to the Hans Lewy Papers Collection number: BANC MSS 91/147 cz The Bancroft Library University of California, Berkeley Berkeley, California Contact Information: The Bancroft Library. University of California, Berkeley Berkeley, California, 94720-6000 Phone: (510) 642-6481 Fax: (510) 642-7589 Email: [email protected] URL: http://bancroft.berkeley.edu Processed by: Ania Laszcz Date Completed: September 2003 Encoded by: James Lake © 2003 The Regents of the University of California. All rights reserved. Collection Summary Collection Title: Hans Lewy papers, Date (inclusive): 1906-1999 Collection Number: BANC MSS 91/147 cz Creator: Lewy, Hans, 1904- Extent: Number of containers: 2 cartons, 1 oversize folderLinear feet: 2.55 linear feet Repository: The Bancroft Library. Berkeley, California 94720-6000 Abstract: Consists of correspondence, writings, teaching materials, and notes relating to Lewy's career as a mathematician in Germany and the United States. Also included are biographical materials and photographs. This collection includes very few materials relating to the Loyalty Oath controversy at UC Berkeley. Physical Location: For current information on the location of these materials, please consult the Library's online catalog. Languages Represented: English Access Collection open for research. -
Notices of the American Mathematical Society ISSN 0002-9920
Notices of the American Mathematical Society ISSN 0002-9920 ABCD springer.com New and Noteworthy from Springer Touching Soap Applied Delay Diff erential Second Edition – Films DVD Equations now in two volumes of the American Mathematical Society A. Arnez , Schönaich, T. Erneux , Université Libre de Bruxelles, Germany; K. Polthier , Belgium Classical Fourier Analysis November 2008 Volume 55, Number 10 Technische Universität Berlin, Germany; This short, expository book off ers a L. Grafakos , University of Missouri, M. Steff ens , C. Teitzel , Unterföhring, collection of examples of delay Columbia, MO, USA Germany diff erential equations which are in use From the reviews of the VHS version as models for a variety of phenomena in 2nd ed. 2008. Approx. 510 p. 10 illus. ... It is recommended to every math- the life sciences, physics and tech- (Graduate Texts in Mathematics, Möbius ematics club and public library, and can nology, chemistry and economics. Volume 249) Hardcover also be used as a source of informa- Avoiding mathematical proofs but ISBN 978-0-387-09431-1 $69.95 Transformations off ering more than 100 illustrations, this tion for university courses in geometry Revealed or calculus of variations. Some topics book illustrates how bifurcation and Modern Fourier Analysis such as building tunnels into minimal asymptotic techniques can be used to L. Grafakos , University of Missouri, page 1226 surfaces are under current mathematical extract analytical information of Columbia, MO, USA research, which makes the tape also physical interest. Written to a multi- worth watching by experts in this eld. disciplinary audience, it sets each area 2nd ed. 2008. Approx. -
Contemporary Mathematics 362
CONTEMPORARY MATHEMATICS 362 Partial Differential Equations and Inverse Problems Pan-American Advanced Studies Institute on Partial Differential Equations, Nonlinear Analysis and Inverse Problems January 6-18, 2003 Santiago, Chile Carlos Conca Raul Man6sevich Gunther Uhlmann Michael S. Vogelius Editors http://dx.doi.org/10.1090/conm/362 Partial Differential Equations and Inverse Problems CoNTEMPORARY MATHEMATICS 362 Partial Differential Equations and Inverse Problems Pan-American Advanced Studies Institute on Partial Differential Equations, Nonlinear Analysis and Inverse Problems January 6-18,2003 Santiago, Chile Carlos Conca Raul Man6sevich Gunther Uhlmann Michael S. Vogelius Editors American Mathematical Society Providence, Rhode Island Editorial Board Dennis DeThrck, managing editor Andreas Blass Andy R. Magid Michael Vogelius This volume represents the Proceedings of the Pan-American Advanced Studies Insti- tute on Partial Differential Equations, Nonlinear Analysis and Inverse Problems held in Santiago, Chile, January 6-18, 2003, with support from the U.S. National Science Foun- dation, the U.S. Department of Energy, the Chilean Conicyt, Centro de mode lamiento Matematico (CMM), and the Canadian Pacific Institute of Mathematical Sciences (PIMS). 2000 Mathematics Subject Classification. Primary 05C40, 35B60, 35B65, 35P25, 35P99, 35Q40, 35Q53, 35Q55, 35Q60, 35R30, 58J05, 78A48, 81Q10, 81U40. Library of Congress Cataloging-in-Publication Data Pan-American Advanced Studies Institute on Partial Differential Equations, Nonlinear Analysis and Inverse Problems (2003 : Santiago, Chile) Partial differential equations and inverse problems : Pan-American Advanced Studies Institute on Partial Differential Equations, Nonlinear Analysis and Inverse Problems, January 6-18, 2003, Santiago, Chile / Carlos Conca ... [et al.], editors. p. em. Includes bibliographical references. ISBN 0-8218-3448-7 (alk.