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math.FA2021
Profile decomposition in Sobolev spaces and decomposition of integral functionals II: homogeneous case
Mizuho Okumura
The present paper is devoted to a theory of profile decomposition for bounded sequences in \emph{homogeneous} Sobolev spaces, and it enables us to analyze the lack of compactness o…
math.FA2021
Profile decomposition in Sobolev spaces and decomposition of integral functionals I: inhomogeneous case
Mizuho Okumura
The present paper is devoted to analysis of the lack of compactness of bounded sequences in \emph{inhomogeneous} Sobolev spaces, where bounded sequences might fail to be compact du…
math.FA2021
Generalization of the Ehrling inequality and universal characterization of completely continuous operators
Mizuho Okumura
The present work is devoted to an extension of the well-known Ehrling inequalities, which quantitatively characterize compact embeddings of function spaces, to more general operato…