Open Problems: Whitney Problems Workshops

Open Problems:

C^m and Sobolev functions on subsets of R^n.
Whitney Extension Problems

 

Many of the problems posed on this webpage were initially formulated at one of the nine workshops dealing with Whitney Extension Problems and related topics:

Whitney Problems Workshops 2008 – 2016

For brief descriptions of this field of research and indications of the importance of its applications we refer to:
http://www.math.technion.ac.il/Site/events/EvntOffices/files/view/cms/104-108-96.pdf

All visitors to this page are warmly invited to submit new problems, and to inform us of any comments or updates that they may have regarding problems which already appear here.
Please send all such material to Pavel Shvartsman  <pshv@tx.technion.ac.il>

It would be very helpful if you can use latex (or some other tex format) and also include your pdf output generated by your (la)tex files.

We hope that the collection of problems and discussions about them that will appear here will significantly stimulate research in the above mentioned topics.

Open Problems: the First Whitney Problems Workshop
August 11-16, 2008, College of William and Mary, Williamsburg, VA, USA
The first Whitney Problems Workshop 2008
Open Problems: the Second Whitney Problems Workshop
August 3-8, 2009, College of William and Mary, Williamsburg, VA, USA
The second Whitney Problems Workshop 2009

Charles Fefferman -A few unsolved problems, June 30, 2016

Recent Publications: 2016

  1. C. Fefferman, A. Israel, K. Luli, “Finiteness Principles for Smooth Selection”.Geom. Funct. Anal. 26 (2016), no. 2, 422 477. http://link.springer.com/article/10.1007%2Fs00039-016-0366-7See also: http://arxiv.org/abs/1603.02323
  2.  C. Fefferman, A. Israel, K. Luli, “Interpolation of data by smooth non-negative functions”,arXiv:1603.02330, March 2016, 26 pp.http://arxiv.org/abs/1603.02330
  3.  A. I. Tyulenev, S. K. Vodop’yanov, “On Whitney-type problem for weighted Sobolev spaces on d-thick closed sets”, arXiv:1606.06749, June 2016, 29 pp. http://arxiv.org/abs/1606.06749
  4.  P. Shvartsman, “Whitney-type extension theorems for jets generated by Sobolev functions”, arXiv:1607.01660, July 2016, 76 pp.  http://arxiv.org/abs/1607.01660
  5.  A. Brudnyi, “On properties of geometric preduals of $C^{k,\omega}$ spaces”,arXiv:1607.04824, July 2016, 28 pp.  https://arxiv.org/abs/1607.04824
  6.  V. I. Burenkov, V. Gol’dshtein, A. Ukhlov, Conformal spectral stability estimates for the Dirichlet Laplacian,Math. Nachr. 288, No. 16, (2015) 1822–1833;  https://arxiv.org/abs/1602.02954
  7. V. Gol’dshtein, A. Ukhlov, On the First Eigenvalues of Free Vibrating Membranes in Conformal Regular Domains,Archive for Rational Mechanics and Analysis, Volume 221, Issue 2,(2016) 893–915;https://arxiv.org/abs/1505.05708
  8.  V. I. Burenkov, V. Gol’dshtein, A. Ukhlov, Conformal spectral stability estimates for the Neumann Laplacian,Math. Nachr. 1–14 (2016) / DOI 10.1002; https://arxiv.org/abs/1602.02954
  9.  V. Gol’dshtein, A. Ukhlov, Spectral estimates of the p-Laplace Neumann operator in conformal regulardomains, Transactions of A. Razmadze Mathematical Institute 170(2016) 137–148                       http://www.sciencedirect.com/science/article/pii/S2346809216000167https: //arxiv.org/abs/1601.01533
  10.  V. Gol’dshtein, A. Ukhlov, Boundary Values of Functions of Dirichlet Spaces $L^1_2$ on Capacitary Boundaries,    https://arxiv.org/abs/1405.3472
  11.  Omer Friedland, Yosef Yomdin, Doubling coverings of algebraichypersurfaces  https://arxiv.org/abs/1512.02903
  12.  Alexander Goncharov, Zeliha Ural, Mityagin’s ExtensionProblem. Progress Report https://arxiv.org/abs/1606.08606
  13.  Daniel Azagra and Carlos Mudarra, “Whitney extension theorems for convex functions of the classes C^1 and C^{1, w}”, to appear in Proc. London Math. Soc.    https://arxiv.org/abs/1507.03931v6
  14. Daniel Azagra and Carlos Mudarra, “An extension theorem for convex functionsof class C^{1,1} on Hilbert spaces”, to appear in J. Math. Anal. Appl.  https://arxiv.org/abs/1603.00241

Recent Publications: 2017

  1. A. I. Tyulenev, S. K. Vodop’yanov,  On a Whitney-type problem for weighted Sobolev spaces on d -thick closed sets  https://arxiv.org/abs/1606.06749v5
  2. V. Gol’dshtein, V. Pchelintsev, A. Ukhlov, Spectral Properties of the Neumann-Laplace operator in Quasiconformal Regular Domains  https://arxiv.org/abs/1703.03577
  3. Vladimir Gol’dshtein, Valerii Pchelintsev, Alexander Ukhlov, Spectral Estimates of the p -Laplace Neumann operator and Brennan’s Conjecture https://arxiv.org/abs/1701.05143
  4. Vladimir Gol’dshtein, Valerii Pchelintsev, Alexander Ukhlov, Integral estimates of conformal derivatives and spectral properties of the Neumann-Laplacian https://arxiv.org/abs/1701.02616
  5. Vladimir Gol’dshtein, Alexander Ukhlov, The spectral estimates for the Neumann-Laplace operator in space domains https://arxiv.org/abs/1607.00487
  6. See also a new version of the paper: V. Gol’dshtein, A. Ukhlov, On the First Eigenvalues of Free Vibrating Membrane in Conformal Regular Domains https://arxiv.org/abs/1505.05708
  7. Daniel Azagra, Erwan Le Gruyer, Carlos Mudarra, Explicit formulas for C^{1,1} and C^{1,ω}_{conv} extensions of 1-jets in Hilbert and superreflexive spaces https://arxiv.org/abs/1706.02235
  8. Daniel Azagra, Carlos Mudarra, Global geometry and C^1 convex extensions of 1-jets https://arxiv.org/abs/1706.09808