This paper deals with the fractional Sobolev spaces W s;p . We analyze the relations among some of their possible denitions and their role in the trace theory. We prove continuous and compact embeddings, investigating the problem of the extension domains and other regularity results. Most of the results we present here are probably well known to the experts, but we believe that our proofs are original and we do not make use of any interpolation techniques nor pass through the theory of Besov spaces. We also present some counterexamples in non-Lipschitz domains.

/pdf/hitchhiker-s-guide-to-the-fractional-sobolev-spaces-irm2sao95g.pdf

Hitchhiker's guide to the fractional Sobolev spaces

关于Semigroups of Linear Operators and Applications to Partial Differential Equations的两个注解

Convex bodies: the brunn–minkowski theory

A review is presented dealing with the use of carbon paste as an electrode maaterial for electrochemical sensors (311 references). It covers mainly publications which appeared during the period 1990–1993; numerous applications demonstrate the widespread applicability of carbon paste in the field of electrochemical analysis, such as voltammetry, amperometry, and potentiometry, but also as an electrode for electrochemical detectors in flow systems.

Sensors based on carbon paste in electrochemical analysis: A review with particular emphasis on the period 1990–1993

Certain conditions for a Riemannian manifold to be isometric with a sphere:Dedicated to Professor Kentaro Yano on his fiftieth birthday

https://web.math.princeton.edu/~chang/11c-mar.pdf

Fractional Laplacian in conformal geometry

In this note, we study the connection between the fractional Laplacian operator that appeared in the recent work of Caffarelli-Silvestre and a class of conformally covariant operators in conformal geometry.

Fractional Laplacian in Conformal Geometry

We investigate the singular sets of solutions of a natural family of conformally covariant pseudodifferential elliptic operators of fractional order, with the goal of developing generalizations of some well-known properties of solutions of the singular Yamabe problem.

Singular Solutions of Fractional Order Conformal Laplacians

Based on the relations between scattering operators of asymptotically hyperbolic metrics and Dirichlet-to-Neumann operators of uniformly degenerate elliptic boundary value problems, we formulate fractional Yamabe problems that include the boundary Yamabe problem studied by Escobar. We observe an interesting Hopf type maximum principle together with interplays between analysis of weighted trace Sobolev inequalities and conformal structure of the underlying manifolds, which extend the phenomena displayed in the classic Yamabe problem and boundary Yamabe problem.

Fractional conformal Laplacians and fractional Yamabe problems

https://upcommons.upc.edu/bitstream/handle/2117/24794/Frank_Gonzalez_Monticelli_Tan.pdf;sequence=1

María del Mar González

Papers

Fractional Laplacian in conformal geometry

Fractional Laplacian in Conformal Geometry

Singular Solutions of Fractional Order Conformal Laplacians

Fractional conformal Laplacians and fractional Yamabe problems

An extension problem for the CR fractional Laplacian