• Corpus ID: 141480115

A study and an application of the concentration compactness type principle

  title={A study and an application of the concentration compactness type principle},
  author={Akasmika Panda and Debajyoti Choudhuri},
  journal={arXiv: Analysis of PDEs},
In this article we develop a concentration compactness type principle in a variable exponent setup. As an application of this principle we discuss a problem involving fractional `{\it $(p(x),p^+)$-Laplacian}' and power nonlinearities with exponents $(p^+)^*$, $p_s^*(x)$ with the assumption that the critical set $\{x\in\Omega:p_s^*(x)=(p^+)^*\}$ is nonempty. 



The concentration-compactness principle for variable exponent spaces and applications

In this paper we extend the well-known concentration -- compactness principle of P.L. Lions to the variable exponent case. We also give some applications to the existence problem for the

On a new fractional Sobolev space and applications to nonlocal variational problems with variable exponent

The content of this paper is at the interplay between function spaces $L^{p(x)}$ and $W^{k, p(x)}$ with variable exponents and fractional Sobolev spaces $W^{s, p}$. We are concerned with some

The concentration-compactness principle for fractional order Sobolev spaces in unbounded domains and applications to the generalized fractional Brezis–Nirenberg problem

In this paper we extend the well-known concentration-compactness principle for the Fractional Laplacian operator in unbounded domains. As an application we show sufficient conditions for the

Multiplicity results for $(p,\, q)$ fractional elliptic equations involving critical nonlinearities.

In this paper we prove the existence of infinitely many nontrivial solutions for the class of $(p,\, q)$ fractional elliptic equations involving concave-critical nonlinearities in bounded domains in

Fractional elliptic problems with critical growth in the whole of $\R^n$

We study the following nonlinear and nonlocal elliptic equation in~$\R^n$ $$ (-\Delta)^s u = \epsilon\,h\,u^q + u^p \ {\mbox{ in }}\R^n, $$ where~$s\in(0,1)$, $n>2s$, $\epsilon>0$ is a small

The Concentration-Compactness Principle in the Calculus of Variations. (The limit case, Part I.)

After the study made in the locally compact case for variational problems with some translation invariance, we investigate here the variational problems (with constraints) for example in RN where the

A Sobolev non embedding

If $\Omega$ is a bounded domain in ${\mathbb R}^n$, $1\le q$<$p\le\infty$ and $s=0,1,2,\ldots$, then clearly $W^{s,p}(\Omega)\subset W^{s,q}(\Omega)$. We prove that this property does not hold when