Lp-estimates for solutions of the heat equation in a dihedral angle

Abstract

We prove coercive weighted Lp-estimates for the solutions of the Dirichlet and Neumann initial-boundary value problems for the heat equation in n-dimensional dihedral angle with arbitrary opening angle θ ∈ (0, 2π]. A crucial role in the proof of this result is played by pointwise estimates of the Green functions of these problems.

Keywords

• parabolic initial boundary value problems
• weighted estimates