-sectoriality of higher-order elliptic systems on general bounded domains
P Tolksdorf - Journal of Evolution Equations, 2018 - Springer
Journal of Evolution Equations, 2018•Springer
On bounded domains\varOmega ⊂ R^ d, d ≥ 2 Ω⊂ R d, d≥ 2, reaching far beyond the
scope of Lipschitz domains, we consider an elliptic system of order 2 m in divergence form
with complex L^ ∞ L∞-coefficients complemented with homogeneous mixed
Dirichlet/Neumann boundary conditions. We prove that the L^ p L p-realization of the
corresponding operator A is R R-sectorial of angle ω ∈ 0, π 2) ω∈ 0, π 2), where in the
case 2 m ≥ d 2 m≥ d, p ∈ (1, ∞) p∈(1,∞), and where p ∈ (2d d+ 2 m-ε, 2d d-2 m+ ε) p∈(2 …
scope of Lipschitz domains, we consider an elliptic system of order 2 m in divergence form
with complex L^ ∞ L∞-coefficients complemented with homogeneous mixed
Dirichlet/Neumann boundary conditions. We prove that the L^ p L p-realization of the
corresponding operator A is R R-sectorial of angle ω ∈ 0, π 2) ω∈ 0, π 2), where in the
case 2 m ≥ d 2 m≥ d, p ∈ (1, ∞) p∈(1,∞), and where p ∈ (2d d+ 2 m-ε, 2d d-2 m+ ε) p∈(2 …
Abstract
On bounded domains , reaching far beyond the scope of Lipschitz domains, we consider an elliptic system of order 2m in divergence form with complex -coefficients complemented with homogeneous mixed Dirichlet/Neumann boundary conditions. We prove that the -realization of the corresponding operator A is -sectorial of angle , where in the case , , and where for some in the case . To perform this proof, we generalize the -extrapolation theorem of Shen to the Banach space-valued setting and to arbitrary Lebesgue-measurable underlying sets.
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