Add to ORKGFor an arbitrary open set Ω ⊂ ℝn we characterize all functions G on the real line such that G o u ∈ W1,p(Ω) for all u ∈ W1,p. New element in the proof is based on Maz'ya's capacitary criterion for the imbedding W1,p(Ω) → L∞(Ω)
In this paper, we establish the existence and continuity of a trace operator for functions of the So...
We characterize the entire functions ℓfor which the induced nonlinear superposition operator f →ℓof ...
We give sufficient conditions for a homogeneous superposition operator to be a continuous mapping be...
AbstractEvery Borel function f : R → R defines a self-map of the space of measurable functions on a ...
International audienceLet $0$<$a$<$1$ and set $\Phi (t)=|t|^a$, $t\in {\mathbb R}$. We prove that th...
In this paper we prove a generalization of the well known theorem of Krasnoselskii on the superposit...
The application of many principles of nonlinear analysis to the study of dif-ferent types of equatio...
AbstractFor an open set Ω⊂Rn let A(Ω) be the space of real analytic functions on Ω. Improving our pr...
In the study of the spaces (formula omitted) of functions for which the pth powers of all the deriv...
In this paper we present a necessary condition for an autonomous superposition operator to act in th...
We study the superposition operators (also called Nemytskii operators) between spaces of almost peri...
AbstractThe main results of this paper are new characterizations of W1,p(Ω), 1<p<∞, and BV(Ω) for Ω⊂...
We give sharp conformal conditions for the dfferentiability in the Sobolev space W1, n-1 loc (Ω,Rn)...
We study the properties of Sobolev functions and mappings, especially we study the violation of some...
Using concentration-compactness arguments, we prove a variant of the Brézis–Lieb-Lemma under weaker ...
In this paper, we establish the existence and continuity of a trace operator for functions of the So...
We characterize the entire functions ℓfor which the induced nonlinear superposition operator f →ℓof ...
We give sufficient conditions for a homogeneous superposition operator to be a continuous mapping be...
AbstractEvery Borel function f : R → R defines a self-map of the space of measurable functions on a ...
International audienceLet $0$<$a$<$1$ and set $\Phi (t)=|t|^a$, $t\in {\mathbb R}$. We prove that th...
In this paper we prove a generalization of the well known theorem of Krasnoselskii on the superposit...
The application of many principles of nonlinear analysis to the study of dif-ferent types of equatio...
AbstractFor an open set Ω⊂Rn let A(Ω) be the space of real analytic functions on Ω. Improving our pr...
In the study of the spaces (formula omitted) of functions for which the pth powers of all the deriv...
In this paper we present a necessary condition for an autonomous superposition operator to act in th...
We study the superposition operators (also called Nemytskii operators) between spaces of almost peri...
AbstractThe main results of this paper are new characterizations of W1,p(Ω), 1<p<∞, and BV(Ω) for Ω⊂...
We give sharp conformal conditions for the dfferentiability in the Sobolev space W1, n-1 loc (Ω,Rn)...
We study the properties of Sobolev functions and mappings, especially we study the violation of some...
Using concentration-compactness arguments, we prove a variant of the Brézis–Lieb-Lemma under weaker ...
In this paper, we establish the existence and continuity of a trace operator for functions of the So...
We characterize the entire functions ℓfor which the induced nonlinear superposition operator f →ℓof ...
We give sufficient conditions for a homogeneous superposition operator to be a continuous mapping be...