Singular solutions of elliptic boundary value problems in polyhedra
Singularities in Muckenhoupt weighted function spaces
We study weighted function spaces of Lebesgue, Besov and Triebel-Lizorkin type where the weight function belongs to some Muckenhoupt class. The singularities of functions in these spaces are characterised by means of envelope functions.
Small global solutions and the nonrelativistic limit for the nonlinear Dirac equation.
In this paper we study the Cauchy problem for the nonlinear Dirac equation in the Sobolev space Hs. We prove the existence and uniqueness of global solutions for small data in Hs with s > 1...
Smooth approximation in weighted Sobolev spaces
We give necessary and sufficient conditions for the equality in weighted Sobolev spaces. We also establish a Rellich-Kondrachov compactness theorem as well as a Lusin type approximation by Lipschitz functions in weighted Sobolev spaces.
Smooth functions and zero traces
Smooth rough paths and applications to Fourier analysis.
Sobolev and isoperimetric inequalities for degenerate metrics.
Sobolev and isoperimetric inequalities for Dirichlet forms on homogeneous spaces
We prove local embeddings of Sobolev and Morrey type for Dirichlet forms on spaces of homogeneous type. Our results apply to some general classes of selfadjoint subelliptic operators as well as to Dirichlet operators on certain self-similar fractals, like the Sierpinski gasket. We also define intrinsic BV spaces and perimeters and prove related isoperimetric inequalities.
Sobolev classes of mappings on a Carnot-Carathéodory space: various norms and variational problems.
Sobolev embeddings for Riesz potentials of functions in grand Morrey spaces of variable exponents over non-doubling measure spaces
Our aim in this paper is to deal with the boundedness of the Hardy-Littlewood maximal operator on grand Morrey spaces of variable exponents over non-doubling measure spaces. As an application of the boundedness of the maximal operator, we establish Sobolev's inequality for Riesz potentials of functions in grand Morrey spaces of variable exponents over non-doubling measure spaces. We are also concerned with Trudinger's inequality and the continuity for Riesz potentials.
Sobolev embeddings for variable exponent Riesz potentials on metric spaces.
Sobolev embeddings with variable exponent
Sobolev inequalities in 2-D hyperbolic space: A borderline case.
Sobolev inequalities on sets with irregular boundaries.
Sobolev inequalities with variable exponent attaining the values 1 and n
Sobolev multipliers
Sobolev regularity via the convergence rate of convolutions and Jensen’s inequality
We derive a new criterion for a real-valued function to be in the Sobolev space . This criterion consists of comparing the value of a functional with the values of the same functional applied to convolutions of with a Dirac sequence. The difference of these values converges to zero as the convolutions approach , and we prove that the rate of convergence to zero is connected to regularity: if and only if the convergence is sufficiently fast. We finally apply our criterium to a minimization...
Sobolev spaces of integer order on compact homogeneous manifolds and invariant differential operators
Let be a Riemannian manifold, which possesses a transitive Lie group of isometries. We suppose that , and therefore , are compact and connected. We characterize the Sobolev spaces
Sobolev spaces on multiple cones
The purpose of this note is to discuss how various Sobolev spaces defined on multiple cones behave with respect to density of smooth functions, interpolation and extension/restriction to/from . The analysis interestingly combines use of Poincaré inequalities and of some Hardy type inequalities.
Sobolev Type Embeddings in the Limiting Case.