### 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%2Fs00039-016-0366-7

See 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 regular

domains, Transactions of A. Razmadze Mathematical Institute 170

(2016) 137–148;

http://www.sciencedirect.com/science/article/pii/S2346809216000167

https://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 algebraic

hypersurfaces

https://arxiv.org/abs/1512.02903

12. Alexander Goncharov, Zeliha Ural, Mityagin’s Extension

Problem. 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 functions

of class C^{1,1} on Hilbert spaces”, to appear in J. Math. Anal. Appl.

https://arxiv.org/abs/1603.00241