Regularity theory for parabolic operators in the half-space with boundary degeneracy

2023/09/25 by Metafune, Giorgio, Negro, Luigi, Spina, Chiara · 1 citation
#35B45 #35J70 #35J75 #35K67 #47D07 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2309.14319

Abstract

We study elliptic and parabolic problems governed by the singular elliptic operators \mathcal L=y^α₁Tr (QD²_xu)+2y^{(α₁+α₂)/(2)}q⋅ ∇_xD_y+γy^α₂ D_yy+Cy^α₂-1D_y under Neumann boundary condition, in the half-space ℝ^N+1₊=\(x,y): x ∈ ℝ^N, y>0\. We prove elliptic and parabolic L^p-estimates and solvability for the associated problems. In the language of semigroup theory, we prove that \mathcal L generates an analytic semigroup, characterize its domain as a weighted Sobolev space and show that it has maximal regularity.

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• Operator Decompositions and Weighted Frame Inequalities for Total Sequences in Hilbert Spaces

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