More on the analysis of local regularity through wavelets

In this paper we want to extend the results of pointwise analysis through wavelet transforms to the class of functions where the local fluctuation is bounded by any submultiplicative function. This generalizez the results obtained before in the well-known case of Hölder regularity.     

Asymmetric Spotty Patterns for the Gray–Scott Model in R2

In this paper, we rigorously prove the existence and stability of asymmetric spotty patterns for the Gray–Scott model in a bounded two-dimensional domain. We show that given any two positive integers   k ₁, k ₂  , there are asymmetric solutions with   k ₁  large spots (type A) and   k ₂  small spots (type B). We also give conditions for their location and calculate their heights. Most of these asymmetric solutions are shown to be unstable. However, in a narrow range of parameters, asymmetric solutions may be stable.