פרופ"ח לביא קרפ

פרופ"ח לביא קרפ

Assoc. Prof. Lavi Karp

פרופ"ח לביא קרפ
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Department
Mathematics
Research Interests
Partial Differential Equations, General Relativity and Potential Theory
Courses
Applied Linear Algebra, Partial Differential Equations, Fourier Series and Integral Transformations
Current Position
Associate Professor, Head of the Department
Contact Information
Email
karp@braude.ac.il
Telephone
972-4-990-1974
Office
EM 405A
Site
http://brd4.braude.ac.il/~karp/
Education
D.Sc.
1992 Pure Mathematics, Technion - Israel Institute of Technology,
B.Sc.
1985 Pure Mathematics, Uppsala University Uppsala, Sweden.
Research Areas

• Cauchy problem for Einstein equations in vacuum and when they are coupled witha perfect fluid. The Euler-Poission e equations. These types of problems involvepartial differential equations of both elliptic and hyperbolic type. The theme is alsorelated to various topics of mathematics and physics, including harmonic analysis,pseudo-differential operators and general relativity.• Free Boundary Problems and Quadrature Domains: These type of problem arerelated to the inverse problem of potential theory. These subjects are also relatedto elliptic partial differential, variational inequalities, Hele-Shaw flows and Pompeiuproblem. In addition, it deals classical theorems going back to Newton’s era.

Academic Appointments
2012-present Head Mathematic Department, ORT Braude College
2011-present Associate Professor, ORT Braude College
2002-2011 Senior Lecturer, ORT Braude College
2001-2007 Adjunct Senior Lecturer, Technion - Israel Institute of
1998-2001 Lecturer, ORT Braude College
Teaching Experience
ORT Braude College:
Applied Linear AlgebraLinear AlgebraCalculus and Analysis in one variableCalculus and Analysis in several variablesOrdinary Differential Equations and Laplace TransformPartial Differential EquationsFunctions Theory (Complex Analysis)Completion Algebra for applied MathematicFourier series and integral transformations
Other Universities:
  • Graduates Courses:Partial Differential Equations, University of StockholmModern Analysis, TechnionTopics in Semi Groups (mini course), Weizmann Institute of Science
  • Undergraduates Courses:Principle of Mathematical Analysis, University of StockholmAlgebra, University of StockholmCalculus and Analysis in one variable, University of StockholmLinear Algebra, TechnionCalculus and Analysis in one variable, TechnionCalculus and Analysis in several variables, TechnionOrdinary Differential Equations, TechnionFunctions Theory (Complex Analysis), TechnionFourier series and Integral Transformations, Technion
Academic and Professional Awards and Grants
2012 ORT Bruade College, Grant for exchanging teaching hours with research
2011 ORT Bruade College, Grant for exchanging teaching hours with research
2010 DFG, Deutsche Forschungsgemeinschaft, Research visit at the
2010 ORT Bruade College, Grant for exchanging teaching hours with research
2008 DFG, Deutsche Forschungsgemeinschaft, Research visit at the
Professional Activities
1991 - 1996 The Center for Gifted Children, Shlomi, Teacher1974 - 1983 Different High Schools in Romania, Teacher
ORT Braude College:
Co-author of Calculus 2 bookletCo- author of Ordinary Differential Equations bookletMember of the Comitee for the Preparation Semester (since 2012)Member of the Comitee for Research of the Center of Teching and Learning (since 2012)Member of the Comitee for Academic Affairs (the last time 2009-2012, 2004-2006)Member of the Comitee for Quality Management (2006-2009)
Reviewing papers for
Int. J. Math. Ed. Sci. Technol., 2012 Int. J. Math. Ed. Sci. Technol. 2011 Int. J. Math. Ed. Sci. Technol. 2010 Int. J. Math. Ed. Sci. Technol. 2009
Reviewing chapters for
"Teaching Mathematics Online: Emergent Technologies and Methodologies", A. Juan, M. A. Huertas, S. Tredholm and C. Stegman (Eds.), Information Science Reference (an imprint of IGI Global), 2012.
Publications
Refereed Papers
  1.  L. Karp, Global solutions to bubble growth in porous media, J. Math. Anal. Appl. 382(2011), 132-139.
  2. U. Brauer and L. Karp, Well-posedness of the Einstein-Euler system in asymptotically flat spacetimes: The constraint equations, Jour. Differential equations 251(2011), 1428-1446.
  3. L. Karp, On the well-posedness of the vacuum Einstein’s equations, Jour. Evolution equations 11 (2011), 641-673.
  4. L. Karp, On null quadrature domains, Computational Methods and Function Theory, 8(2008) No. 1, 57-72.
  5. U. Brauer and L. Karp, Local existence of classical solutions for the Einstein-Euler system using weighted Sobolev spaces of fractional order, C. R. Acad. Sci. Paris, Ser. I345(2007), 49-54.
  6. L. Karp, Multivalid analytic continuation of the Cauchy transform, Potential Analysis, 24(2006), 1-13.
  7. W. K. Hayman, L. Karp and H.S. Shapiro, Newtonian capacity and quasi balayage, Rend. Mat. Appl. 20 No. 7(2000), 93-129.
  8. L. Karp and H. Shahgholian, Regularity of a free boundary problem near the infinity point, Comm. Partial Differential Equations 25 No.11- 12(2000), 2055-2086.
  9. L. Karp, T. Kilpel ¨ainen, A. Petrsyan and H. Shahgholian, On the porosity of Free boundaries in degenerate variational inequalities, Jour. Differential Equations 164 No. 1(2000), 110-117.
  10. L. A. Caffarelli, L. Karp and H. Shahgholian, Regularity of a free boundary problem with application to the Pompeiu problem, Ann. of Math. 151 No.1 (2000), 269-292.
  11. L. Karp and H. Shahgholian, On the optimal growth of functions with bounded laplacian, Electronic J. Differential Equations 2000 No. 03(2000), 1-9.
  12. L. Karp and H. Shahgholian, Regularity of a free boundary problem, Jour. Geometrical Anal. 9 No. 4 (1999), 653-669.
  13. L. Karp and A. Margulis, Newtonian potential theory for unbounded sources and applications to free boundary problems, Journal d’Analyse Math´ematique 70 (1996), 1-63.
  14. L. Karp, Liouville-type theorems for second order elliptic differential equations, Ann. Scuola Norm. Sup. Pisa 22 (1995), 275-298.
  15. L. Karp, On the Newtonian potential for ellipsoids, Complex Variables and Elliptic Equations 25 (1995), 367-372.
  16. L. Karp, Generalized Newton potential and its applications, Jour. Math. Anal. Appl. 174 (1993), 480-497.
  17. L. Karp, Construction of quadrature domains in Rn from quadrature domains in R2, Complex Variables and Elliptic Equations 17(1992), 179-189.

Accepted

  1. L. Karp A Margulis, Null quadrature domains and a free boundary problem for the Laplacian, Indiana University Mathematics Journal.Submittedpapers

Submitted papers

  1. U. Brauer and L. Karp, Local existence of solutions of self gravitating relativistic perfect fluids, Comm. Math. Physics, 32 pp.
  2. U. Brauer and L. Karp, Elliptic Equations in Weighted Besov Spaces on Asymptotically Flat Riemannian Manifolds, 27 pp.
Books
  1. M. Agranovsky, M. Ben-Artzi, G. Galloway, L. Karp, S. Reich, D. Shoikhet, G. Weinstein and L. Zalcman (Editors), Complex Analysis and Dynamical Systems IV: Part 2. General Relativity, Geometry, and PDE, Contemporary Mathematics vol. 554, American Mathematical Society, 2011.
  2. M. Agranovsky, M. Ben-Artzi, G. Galloway, L. Karp, S. Reich, D. Shoikhet, G. Weinstein and L. Zalcman (Editors), Complex Analysis and Dynamical Systems IV: Part 1. Function Theory and Optimization, Contemporary Mathematics vol. 553, American MathematicalSociety 2011.
  3. M. Agranovsky, D. Bshouty, L.Karp, S. Reich, D. Shoikhet and L. Zalcman (Editors), Proceedings of an international conference Complex Analysis and Dynamical System III, a conference in honor of the Retirement of Dov Aharonov, Lev Aizenberg, Samuel Krushkal, and Uri Srebro, Contemporary Mathematics, Vol.455, American MathematicalSociety 2008.
  4. M. Agranovsky, L.Karp and D. Shoikhet and (Editors), Proceedings of an international conference Complex Analysis and Dynamical System II, a conference in honor of Professor Lawrence Zaclman 60th birthday, Contemporary Mathematics, Vol 382, American Mathematical Society 2005.
  5.  M. Agranovsky, L.Karp, D. Shoikhet and and L. Zalcman, (Editors), Proceedings of an international conference Complex Analysis and Dynamical Systems, Contemporary Mathematics Vol. 364, American Mathematical Society 2004.

In Preparation

  1. L. Karp A. S. Margulis, Characterization of null quadrature domains with a complement in a strip.
  2. U. Brauer and L. Karp, Elliptic equations on Riemannian manifolds in weighted Besov spaces
  3. L. Karp A. S. Margulis, Non-uniqueness of quadrature domains
  4. L. Karp and H. Shahgholian, On the negative set of the Schwarz potential
  5. L. Karp and V. Ostrovsky, Characteristic approach to Einstein constraints equations.
  6. U. Brauer and L. Karp, Local existence of Euler-Poisson equation.
  7. U. Brauer and L. Karp, Einstein-Euler systems with polytropic equations of state.
Conference Proceedings and Abstracts
Conference and Proceedings Referred Papers
  1. L. Karp and H.S. Shapiro, Isolated Singularities of Harmonic Functions, Modern Developments in Multivariate Approximation, W. Hausmann, K. Jetter, M. Reimer and J. St ¨ocker editors, Birkh¨auser (2003), 165- 174.

Conference and Proceedings

  1. L. Karp, A question on the regularity of the boundary of a quadrature domain, In Quadrature and Applications, A Harold Shapiro Anniversary Volume, Editors P. Epenfelet, B.Gustafsson, D. Khavinsson and M. Putinar, Birkh¨auser 2005, 2 pp.
Other Publications
Unpublished papers and Professional Reports
  1. A. Goldvard and L. Karp, Applications of matrices multiplication to determinant and rotations formulas in Rn, in http://arxiv.org/abs/1010.3729, 10 pp.
  2. U. Brauer and L.Karp, Well-posedness of the Einstein-Euler system in asymptotically flat spacetimes, inhttp://adsabs.harvard.edu/abs/2008arXiv0810.5045B, 76 pp.
  3. U. Brauer and L.Karp, Interpolation of nonlinear contractive operators, Preprint, 4 pp.
  4. U. Brauer and L.Karp, Weighted Space (The Galilee Center for Applied Mathematics), 10 pp.
  5. L. Karp, Asymptotic Properties of Unbounded Quadrature Domains, (a research proposal), 8 pp.
  6. L. Karp, The Cauchy problem for Einstein vacuum equations: a simultaneous study of the constraints and evolutions equations, (a research proposal) 6 pp.
  7. U. Brauer and L.Karp, Application of Weighted Sobolev spaces of fractional order to Einstein’s Equations (a research proposal), 9 pp.
  8. L.Karp, Some Mathematical aspects of General Relativity (a research . proposal), 13 pp.
  9. L.Karp, The Initial Value Problem for the Einstein-Euler System in Weighted Fractional Sobolev Spaces (a research proposal), 4 pp.
  10. A. Goldvard and L.Karp, Lectures notes in applied Linear Algebra (in Hebrew, can be found in College’s website, courses number 11002 and 11020).