Add to ORKGInternational audienceLet $0$<$a$<$1$ and set $\Phi (t)=|t|^a$, $t\in {\mathbb R}$. We prove that the superposition operator $u\mapsto \Phi (u)$ maps the Sobolev space $W^{1,p}({\mathbb R}^n)$ into the fractional Sobolev space $W^{a,p/a}({\mathbb R}^n)$. We also investigate the case of more general nonlinearities
AbstractWe characterize the pointwise multipliers which maps a Sobolev space H˙r(Rd) to a Sobolev sp...
Using concentration-compactness arguments, we prove a variant of the Brézis–Lieb-Lemma under weaker ...
AbstractThis paper deals with the fractional Sobolev spaces Ws,p. We analyze the relations among som...
International audienceLet $0$<$a$<$1$ and set $\Phi (t)=|t|^a$, $t\in {\mathbb R}$. We prove that th...
For an arbitrary open set Ω ⊂ ℝn we characterize all functions G on the real line such that G o u ∈ ...
Y.H. would like to thank IHE ́S for their hospitality and support while he visited in the summer of ...
This paper deals with the fractional Sobolev spaces W^[s,p]. We analyze the relations among some of ...
On the differentiability of the superposition operator in Hölder and Sobolev spaces. - In: Nonlinear...
We characterize the entire functions ℓfor which the induced nonlinear superposition operator f →ℓof ...
AbstractThe article is concerned with the Bourgain, Brezis and Mironescu theorem on the asymptotic b...
$ (-\varDelta)_{p(\cdot)}^{s(\cdot)}u+V(x)|u|^{p(x)-2}u = f(x,u)+g(x) $ where $ x\in\Omega\subs...
International audienceWe illustrate the crucial importance of the Hardy type inequalities in the stu...
International audienceWe may always decompose any function $f\in W^{1,p}({\mathbb R}^N)$ as $f=g+h$ ...
In the study of the spaces (formula omitted) of functions for which the pth powers of all the deriv...
This paper deals with the fractional Sobolev spaces W-s,W-p. We analyze the relations among some of ...
AbstractWe characterize the pointwise multipliers which maps a Sobolev space H˙r(Rd) to a Sobolev sp...
Using concentration-compactness arguments, we prove a variant of the Brézis–Lieb-Lemma under weaker ...
AbstractThis paper deals with the fractional Sobolev spaces Ws,p. We analyze the relations among som...
International audienceLet $0$<$a$<$1$ and set $\Phi (t)=|t|^a$, $t\in {\mathbb R}$. We prove that th...
For an arbitrary open set Ω ⊂ ℝn we characterize all functions G on the real line such that G o u ∈ ...
Y.H. would like to thank IHE ́S for their hospitality and support while he visited in the summer of ...
This paper deals with the fractional Sobolev spaces W^[s,p]. We analyze the relations among some of ...
On the differentiability of the superposition operator in Hölder and Sobolev spaces. - In: Nonlinear...
We characterize the entire functions ℓfor which the induced nonlinear superposition operator f →ℓof ...
AbstractThe article is concerned with the Bourgain, Brezis and Mironescu theorem on the asymptotic b...
$ (-\varDelta)_{p(\cdot)}^{s(\cdot)}u+V(x)|u|^{p(x)-2}u = f(x,u)+g(x) $ where $ x\in\Omega\subs...
International audienceWe illustrate the crucial importance of the Hardy type inequalities in the stu...
International audienceWe may always decompose any function $f\in W^{1,p}({\mathbb R}^N)$ as $f=g+h$ ...
In the study of the spaces (formula omitted) of functions for which the pth powers of all the deriv...
This paper deals with the fractional Sobolev spaces W-s,W-p. We analyze the relations among some of ...
AbstractWe characterize the pointwise multipliers which maps a Sobolev space H˙r(Rd) to a Sobolev sp...
Using concentration-compactness arguments, we prove a variant of the Brézis–Lieb-Lemma under weaker ...
AbstractThis paper deals with the fractional Sobolev spaces Ws,p. We analyze the relations among som...