Sobolev embeddings, extensions and measure density condition

2008/02/01 by Piotr Hajłasz, Pekka Koskela, Heli Tuominen · 151 citations
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analytic and geometric function theory #Corollary #Discrete mathematics #Domain (mathematical analysis) #Embedding #Ergodic theory #Extension (predicate logic) #Invariant (physics) #Invariant measure #Lipschitz continuity #Mathematical analysis #Mathematical physics #Mathematics #Measure (data warehouse) #Nonlinear Partial Differential Equations #Pure mathematics #Sobolev inequality #Sobolev space

paper · pdf · doi:10.1016/j.jfa.2007.11.020

published in Journal of Functional Analysis 254(5), 1217-1234 (Elsevier BV)

openalex publication_date 2008/02/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/02

Cited by

• Robin harmonic measure with a variable permeability parameter
• Sobolev extension via reflections
• Helmholtz transmission problem and intrinsic impedance scattering problem on extension domains
• The Relative Capacity
• Continuous differentiability of the signum function and Newton's method for bang-bang control
• Product of extension domains is still an extension domain
• On analysis of problems of mathematical physics with non-Lipschitz boundaries
• Infinity thick quasiconvexity and applications
• Sobolev embedding for M^1,p spaces is equivalent to a lower bound of the measure
• Geometric characterizations of embedding theorems
• Optimal absorption of acoustical waves by a boundary
• A necessary condition on domains for optimal Orlicz-Sobolev embeddings
• Diffusion over ramified domains: solvability and fine regularity
• Smoothness spaces of higher order on lower dimensional subsets of the Euclidean space
• Regularity and continuity of local Multilinear Maximal type operator
• Bi-Lipschitz invariance of planar BV- and W^1,1-extension domains
• On Sobolev extension domains in Rⁿ
• Generalization of Rellich-Kondrachov theorem and trace compacteness in the framework of irregular and fractal boundaries
• Dirichlet-to-Neumann or Poincaré-Steklov operator on fractals described by d -sets
• How to recognize polynomials in higher order Sobolev spaces
• C^1,ω extension formulas for 1-jets on Hilbert spaces
• Existence of optimal shapes for heat diffusions across irregular interfaces
• Poincaré-Steklov operator and Calderón's problem on extension domains
• The extension property for domains with one singular point
• Sobolev embedding implies regularity of measure in metric measure spaces
• The square root problem for second order, divergence form operators with mixed boundary conditions on L^p
• Fractal zeta functions and complex dimensions of relative fractal drums
• Interpolation Theory for Sobolev Functions with Partially Vanishing Trace on Irregular Open Sets