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Fractional variable exponents Sobolev trace spaces and Dirichlet problem for the regional fractional p(.) -Laplacian
In this paper we give a finer analysis of fractional variable exponents Sobolev spaces. We use the relative capacity to characterize completely the...
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Sharp Critical and Subcritical Trace Trudinger–Moser and Adams Inequalities on the Upper Half-Spaces
In this paper, we establish the sharp critical and subcritical trace Trudinger–Moser and Adams inequalities on the half-spaces and prove the...
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Borderline Case of Traces and Extensions for Weighted Sobolev Spaces
In this paper, we study the traces and the extensions for weighted Sobolev spaces on upper half spaces when the weights reach to the borderline...
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Sobolev Spaces
Contact and friction problems, as well as many other problems involving elliptic partial differential equations and some specific boundary...
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Dixmier-type traces on symmetric spaces associated with semifinite von Neumann algebras
We prove that a normalised linear functional on certain symmetric spaces associated with a semifinite von Neumann algebra, respects tail majorisation...
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Reasonable state spaces
Lucien Hardy laid out a program for deducing state spaces from reasonable axioms, and thereby derived classical and quantum physics (QP). In a level N ...
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The trace space of anisotropic least gradient functions depends on the anisotropy
We study the set of possible traces of anisotropic least gradient functions. We show that even on the unit disk it changes with the anisotropic norm:...
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Nuclear Embeddings of Morrey Sequence Spaces and Smoothness Morrey Spaces
We study nuclear embeddings for spaces of Morrey type, both in its sequence space version and as smoothness spaces of functions defined on a bounded...
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Banach Spaces
This chapter explores the properties of operators and functionals on general Banach spaces, with the aim of generalizing various results on Hilbert...
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Sobolev spaces
Sobolev spaces were introduced by Sergei Lvovich Sobolev in the 1930s, and have since been widely embraced and developed by other mathematicians....
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p-Harmonic map**s between metric spaces
In this paper, we solve the Dirichlet problem for Sobolev maps between singular metric spaces that extends the corresponding result of Guo and Wenger...
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Multidimensional Sobolev Spaces
We have introduced one-dimensional Sobolev spaces in Chap. 2 . The fundamental concept that is...
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Metric Spaces
In the previous chapters, we have introduced the concept of topological space, as well as a variety of concepts related to proximity. Following our...
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Symmetric Spaces Rolling on Flat Spaces
The objective of the current paper is essentially twofold. Firstly, to make clear the difference between two notions of rolling a Riemannian manifold...
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Existence of Solutions in the Trace Sense
In previous Chapters, we introduced two different notions of solutions to the least gradient problem. In Chap. 1, we understood the boundary...