The Leibniz rule for the Dirichlet and the Neumann Laplacian
The Leibniz rule for the Dirichlet and the Neumann Laplacian
We study the bilinear estimates in the Sobolev spaces with the Dirichlet and the Neumann boundary condition. The optimal regularity is revealed to get such estimates in the half space case, which is related to not only smoothness of functions and but also boundary behavior. The crucial point for the …