Anisotropic Hörmander Spaces on the Lateral Surface of a Cylinder

详细

We introduce a class of anisotropic inner-product Hörmander spaces on the smooth lateral surface of a cylinder. These spaces do not depend on the choice of special local coordinates on the surface and can be obtained by interpolation with a function parameter between pairs of anisotropic Sobolev spaces. The introduced spaces naturally appear in the theory of parabolic differential equations.