Filling a possible gap in the literature, we give a complete and readable proof of this trace theorem, which also shows that the imbedding constant is uniformly bounded for $T ↓ 0$ . The proof is based on a version of Hardy’s inequality (cp. Appendix).

Maximal regularity for parabolic equations with inhomogeneous boundary conditions in Sobolev spaces with mixed $L_{p}$ -norm.

Weidemaier, Peter — 2002

Electronic Research Announcements of the American Mathematical Society [electronic only]

Page 1

Download Results (CSV)

Advanced Search

Formula preview

Currently displaying 1 – 5 of 5

Refinement of an Lp-Estimate of Solonnikov for a Parabolic Equation of the Second Order with Conormal Boundary Condition.

Existence of Regular Solutions for a Quasilinear Wave Equation with the Third Boundary Condition.

On the trace theory for functions in Sobolev spaces with mixed L p -norm

The trace theorem W p 2 , 1 ( Ω T ) ∋ f ↦ ∇ x f ∈ W p 1 - 1 / p , 1 / 2 - 1 / 2 p ( ∂ Ω T ) revisited

Maximal regularity for parabolic equations with inhomogeneous boundary conditions in Sobolev spaces with mixed L p -norm.

On the trace theory for functions in Sobolev spaces with mixed $L_{p}$ -norm

The trace theorem $W_{p}^{2, 1} (Ω_{T}) ∋ f \mapsto \nabla_{x} f \in W_{p}^{1 - 1 / p, 1 / 2 - 1 / 2 p} (\partial Ω_{T})$ revisited

Maximal regularity for parabolic equations with inhomogeneous boundary conditions in Sobolev spaces with mixed $L_{p}$ -norm.