6533b7d3fe1ef96bd12600f2

RESEARCH PRODUCT

Dimension estimates for the boundary of planar Sobolev extension domains

Tapio RajalaDanka LučićJyrki Takanen

subject

Applied MathematicsMathematical analysisBoundary (topology)Extension (predicate logic)Physics::Classical PhysicsFunctional Analysis (math.FA)Sobolev spaceMathematics - Functional AnalysisPlanarDimension (vector space)46E35 28A75Mathematics - Classical Analysis and ODEsBounded functionClassical Analysis and ODEs (math.CA)FOS: MathematicsAnalysisMathematics

description

We prove an asymptotically sharp dimension upper-bound for the boundary of bounded simply-connected planar Sobolev $W^{1,p}$-extension domains via the weak mean porosity of the boundary. The sharpness of our estimate is shown by examples.

yearjournalcountryeditionlanguage
2020-06-25
http://arxiv.org/abs/2006.14213