Related papers: Removability: First order Sobolev space, PDE solut…
In this article some explicit estimates on the decay of the convolutive inverse of a sequence are proved. They are derived from the functional calculus for Sobolev algebras. Applications include localization in spline-type spaces and…
A holistic view of the cosmological appearance and development of space is obtained by studying space as a spherically closed surface of a 4-sphere in a zero energy balance between motion and gravitation. Such an approach re-establishes…
We present the unique solvability in Sobolev spaces of time fractional parabolic equations in divergence and non-divergence forms. The leading coefficients are merely measurable in $(t,x_1)$ for $a^{ij}$, $1 \leq i,j \leq d$, $(i,j) \neq…
In recent years, progress toward the classification of superintegrable systems with higher order integrals of motion has been made. In particular, a complete classification of all exotic potentials with a third or a fourth order integrals,…
We study reparametrization invariant Sobolev metrics on spaces of regular curves. We discuss their completeness properties and the resulting usability for applications in shape analysis. In particular, we will argue, that the development of…
We extend the result of D. Phillips (On one-homogeneous solutions to elliptic systems in two dimensions. C. R. Math. Acad. Sci. Paris 335 (2002), no. 1, 39-42) by showing that one-homogeneous solutions of certain elliptic systems in…
The article is devoted to the existence of solutions of a certain system of quadratic integral equations in H^1(R, R^N). We show the existence of a perturbed solution by using a fixed point technique in the Sobolev space on the real line.
New embeddings of weighted Sobolev spaces are established. Using such embeddings, we obtain the existence and regularity of positive solutions with Navier boundary value problems for a weighted fourth order elliptic equation. We also obtain…
We consider uniformly elliptic and parabolic second-order equations with bounded zeroth-order and bounded VMO leading coefficients and possibly growing first-order coefficients. We look for solutions which are summable to the $p$-th power…
In this paper we present a weighted $L_p$-theory of parabolic systems on a half space. The leading coefficients are assumed to be only measurable in $t$ and have small bounded mean oscillations (BMO) with respect to $x$, and the lower order…
We study the Laplace operator on domains subject to Dirichlet or Neumann boundary conditions. We show that these operators admit a bounded $H^{\infty}$-functional calculus on weighted Sobolev spaces, where the weights are powers of the…
We obtain improved fractional Poincar\'e and Sobolev Poincar\'e inequalities including powers of the distance to the boundary in John, $s$-John domains and H\"older-$\alpha$ domains, and discuss their optimality.
We consider the one-dimensional Vlasov equation with an attractive cosine potential, and its non homogeneous stationary states that are decreasing functions of the energy. We show that in the Sobolev space $W^{1,p}$ ($p>2$) neighborhood of…
Optimal higher-order Sobolev type embeddings are shown to follow via isoperimetric inequalities. This establishes a higher-order analogue of a well-known link between first-order Sobolev embeddings and isoperimetric inequalities. Sobolev…
We prove that weakly differentiable weights $w$ which, together with their reciprocals, satisfy certain local integrability conditions, admit a unique associated first-order $p$-Sobolev space, that is \[H^{1,p}(\mathbb{R}^d,w\,\d…
We prove the transitivity of real Anosov diffeomorphisms, which are Anosov diffeomorphisms where stable and unstable spaces decompose into a continuous sum of invariant one-dimensional sub-spaces with uniform contraction/expansion over the…
In this paper, we investigate in detail a superintegrable extension of the singular harmonic oscillator whose wave functions can be expressed in terms of exceptional Jacobi polynomials. We show that this Hamiltonian admits a fourth-order…
Using a generalization of complexes, called 2-complexes, this paper defines and analyzes new Sobolev spaces of matrix fields and their interrelationships within a commuting diagram. These spaces have very weak second-order derivatives. An…
The theme of this short article is to investigate an orthogonal decomposition of a Sobolev space and look at some properties of the inner product therein and the distance defined from the inner product. We also determine the dimension of…
We consider both divergence and non-divergence parabolic equations on a half space in weighted Sobolev spaces. All the leading coefficients are assumed to be only measurable in the time and one spatial variable except one coefficient, which…