7

I would like to create a "big-list" of resources (e.g., survey papers, webpages, conference proceedings, monographs, etc.) that collect and offer some context and overviews of:

open problems, conjectures, and questions that have recently arisen in nonlinear analysis.

Side note: In particular(*), I'm very curious about "what's going on" in nonlinear elliptic PDE, nonlinear hyperbolic equations, solitary waves, Lagrangian and Hamiltonian Systems, and Maxwell's equations.

(*)But this should not be seen as a restriction if you have good material to share on other related topics.

Andrews
  • 4,293
Dal
  • 8,582
  • By the way, a list of some open problems in PDE appered today in arXiv - http://arxiv.org/pdf/1512.06540v1.pdf You may find some of them interesting. – Voliar Dec 22 '15 at 18:43

1 Answers1

2

Let me provide a few references about the $p$-Laplace operator.

  1. Some open problems concerning $p$-Laplacian are listed in Abstracts of Mini-Workshop "The p-Laplacian Operator and Applications", 2013, on the pages 476-480. (Problem 3 about Nodal line of second $p$-eigenfunction is explained also here, p. 10.)

  2. Other open problems like a unique continuation property can be found in classical book Notes on the $p$-Laplace equation, by P. Lindqvist, p. 70.

  3. Some open questions on the Fredholm alternative for $p$-Laplacian are discussed in this article.

Voliar
  • 1,595