Some Sobolev embeddings of fractional type and applications
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Date
2024-06
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Publisher
University of M’sila, Faculty of Mathematics and Computer Science, Department of Mathematics
Abstract
Using the Riemann-Liouville derivatives as a basis, we let us introduce in depth fractional Sobolev spaces, characterizing their distinctive nature. We also define derivatives
weak fractional values and demonstrate their agreement with the derivatives of RiemannLiouville. Subsequently, we established the equivalence between certain norms within
these spaces, thus deducing their exhaustiveness, reflexivity, and separability. In an unconventional way, we highlight certain Sobolev embeddings which are not generally classical, thus enriching our understanding of these spaces. Finally, we apply these notions
to a specified boundary problem.
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Keywords
Sobolev spaces of fractional order, Riemann-Liouville, Sobolev injections