Increased Integrability of the Gradient of the Solution to the Zaremba Problem for the Poisson Equation

An estimate is obtained for the increased integrability of the gradient of the solution to the Zaremba problem in a bounded plane domain with a Lipschitz boundary and rapidly alternating Dirichlet and Neumann boundary conditions, with an increased integrability exponent independent of the frequency of the boundary condition change.

Automated summary

The study provides an estimate for the increased integrability of the gradient of the solution to the Zaremba problem in a bounded plane domain with a Lipschitz boundary and rapidly alternating Dirichlet and Neumann boundary conditions, with the increased integrability exponent being independent of the frequency of the boundary condition change.