Regularity of weak solutions under pure order differential operators by means of the continuous wavelet transform with rotations

Abstract

By introducing a rotation parameter besides translations and dilations, the continuous wavelet transform has been defined with respect to an admissible function not necessarily radial to study the local regularity of weak solutions [Formula: see text] under [Formula: see text], where [Formula: see text] is of class [Formula: see text] in a neighborhood of some point [Formula: see text] in [Formula: see text], and [Formula: see text] is a partial differential operator of order [Formula: see text]. The method used to study this fact is through the local convergence of the continuous wavelet transform.