Hilbert complexes with mixed boundary conditions part 3: Biharmonic complexes Article Swipe

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Biharmonic equation Mathematics Lipschitz continuity Sobolev space Bounded function Boundary (topology) Pure mathematics Sobolev spaces for planar domains Order (exchange) Mathematical analysis Lipschitz domain Boundary value problem Hilbert space Functional analysis Interpolation space Economics Gene Biochemistry Finance Chemistry

Dirk Pauly , Michael Schomburg ·

YOU? · · 2023 · Open Access · · DOI: https://doi.org/10.1002/mma.9437 · OA: W4388447314

We show that the biharmonic Hilbert complex with mixed boundary conditions on bounded strong Lipschitz domains is closed and compact. The crucial results are compact embeddings that follow by abstract arguments using functional analysis together with particular regular decompositions. Higher Sobolev order results are also proved.