Anisotropic curl-free wavelets with boundary conditions

This paper deals with the construction of anisotropic curl-free wavelets that satisfy the tangent boundary conditions on bounded domains. Based on some assumptions, we first obtain the desired curl-free Riesz wavelet bases through the orthogonal decomposition of vector-valued L2. Next, the characterization of Sobolev spaces is studied. Finally, we give the concrete construction of wavelets satisfying the initial assumptions.