On the behavior of solutions of elliptic and parabolic equations at a crack (Q803787)

The Dirichlet problem for linear elliptic equations is investigated in domains with cracks, i.e., in domains where boundary sections meet at an angle of degree \(2\pi\). The result is that the solution is then Hölder continuous up to the boundary with any exponent strictly less than 1/2. A corresponding result holds for the initial boundary value problem for linear parabolic equations.