A unified approach to degenerate problems in the half-space

We study elliptic and parabolic problems governed by the singular elliptic operatorsL=yα1Δx+yα2(Dyy+cyDy−by2),α1,α2∈R in the half-space R+N+1={(x,y):x∈RN,y>0}. We prove elliptic and parabolic Lp-estimates and solvability for the associated problems. In the language of semigroup theory, we prove t...

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Bibliographic Details
Published in:Journal of Differential Equations 2023-04, Vol.351, p.63-99
Main Authors: Metafune, G., Negro, L., Spina, C.
Format: Article
Language:English
Subjects:
Boundary degeneracy
Degenerate elliptic operators
Maximal regularity
Vector-valued harmonic analysis
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Summary:We study elliptic and parabolic problems governed by the singular elliptic operatorsL=yα1Δx+yα2(Dyy+cyDy−by2),α1,α2∈R in the half-space R+N+1={(x,y):x∈RN,y>0}. We prove elliptic and parabolic Lp-estimates and solvability for the associated problems. In the language of semigroup theory, we prove that L generates an analytic semigroup, characterize its domain as a weighted Sobolev space and show that it has maximal regularity.
ISSN:0022-0396
1090-2732
DOI:10.1016/j.jde.2022.12.018