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math.CA2013★ 1 cited
Solvability of the divergence equation implies John via Poincaré inequality
Renjin Jiang, Aapo Kauranen, Pekka Koskela
Let $Ω\subset \rr^2$ be a bounded simply connected domain. We show that, for a fixed (every) $p\in (1,\fz),$ the divergence equation is solvable in $W^…
math.CA2013★ 1 cited
Korn inequality on irregular domains
Renjin Jiang, Aapo Kauranen
In this paper, we study the weighted Korn inequality on some irregular domains, e.g., -John domains and domains satisfying quasi-hyperbolic boundary conditions. Examples regardi…
math.CA2013★ 6 cited
Boundary blow up under Sobolev mappings
Aapo Kauranen, Pekka Koskela
We prove that for mappings continuous up to the boundary, with modulus of continuity satisfying certain divergence condition, the image of the boundary of the…