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We are concerned with scalar valued local parabolic quasi-minimizers u associated to a Carathéodory integrand f obeying p -growth assumptions for p > 1 . For such parabolic quasi-minimizers we prove local Hölder continuity provided they are already locally bounded. The superquadratic case p ≥ 2 has already been considered in [17,22] , whereas the subquadratic case could, at least to our knowledge, not be treated in the past. In this paper we are able to handle both the sub- and superquadratic case under more general growth conditions. [ABSTRACT FROM AUTHOR]

In this work, we analytically investigate a multi-component system for describing phase separation and damage processes in solids. The model consists of a parabolic diffusion equation of fourth order for the concentration coupled with an elliptic system with material dependent coefficients for the strain tensor and a doubly nonlinear differential inclusion for the damage function. The main aim of this paper is to show existence of weak solutions for the introduced model, where, in contrast to existing damage models in the literature, different elastic properties of damaged and undamaged material are regarded. To prove existence of weak solutions for the introduced model, we start with an approximation system. Then, by passing to the limit, existence results of weak solutions for the proposed model are obtained via suitable variational techniques. [ABSTRACT FROM AUTHOR]