The Trace Theorem for Anisotropic Sobolev — Slobodetskii Spaces with Applications to Nonhomogeneous Elliptic BVPs

The Trace Theorem for Anisotropic Sobolev — Slobodetskii Spaces with Applications to Nonhomogeneous Elliptic BVPs Full article

Journal

Известия Алтайского государственного университета. Физико-математические науки

Output data

Year: 2018, Number: 4(102), Pages: 102-107 Pages count : 6 DOI: 10.14258/izvasu(2018)4-19

Tags

anisotropic fractional Sobolev spaces, boundary trace of function, p-Laplace operator

Authors

Sazhenkov S.A. ^1,2,3 , Sazhenkova E.V. ⁴

Affiliations

1	Lavrentiev Institute of Hydrodynamics of the Siberian Branch of the RAS
2	Novosibirsk State University
3	Heilongjiang University, Sino-Russian Institute
4	Novosibirsk State University of Economics and Management

Anisotropic Sobolev — Slobodetskii spaces in poly-cylindrical domains of any dimension N are considered. In the first part of the article we revisit the well-known Lions — Magenes Trace Theorem (1961) and naturally extend regularity results for the trace and lift operators onto anisotropic case. As a byproduct, we build some generalization of the Kruzhkov — Korolev Trace Theorem for the first-order Sobolev Spaces (1985). In the second part of the article we observe the nonhomogeneous Dirichlet, Neumann, and Robin problems for p-elliptic equations. The well-posedness theory for these problems can be successfully constructed using isotropic theory, and the corresponding results are outlined in the article. Clearly, in such a unilateral approach the anisotropic features are ignored and the results are far beyond the critical regularity. In the article, the refinement is fulfilled with the help of the constructed extension. Namely, we formulate proper weakly regular anisotropic classes for boundary conditions, such that the boundary value problems appear to be well-posed. In the end of the article, the analogous results are formulated for the p-parabolic problems.

Sazhenkov S.A. , Sazhenkova E.V.
The Trace Theorem for Anisotropic Sobolev — Slobodetskii Spaces with Applications to Nonhomogeneous Elliptic BVPs
Известия Алтайского государственного университета. Физико-математические науки. 2018. N4(102). P.102-107. DOI: 10.14258/izvasu(2018)4-19 РИНЦ OpenAlex

Published print:

Sep 11, 2018

Elibrary:	35647394
OpenAlex:	W2899772816

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