These lecture notes offer a self-contained advent to regularity thought for elliptic equations and structures in divergence shape. After a brief evaluate of a few classical effects on all over the place regularity for scalar-valued susceptible strategies, the presentation makes a speciality of vector-valued susceptible options to a approach of a number of coupled equations. within the vectorial case, vulnerable recommendations could have discontinuities and so are anticipated, mostly, to be general merely outdoors of a suite of degree 0. a number of tools are awarded about the evidence of such partial regularity effects, and optimum regularity is mentioned. ultimately, a quick evaluate is given at the present state-of-the-art in regards to the dimension of the singular set on which discontinuities may possibly occur.
The notes are meant for graduate and postgraduate scholars with a great historical past in useful research and a few familiarity with partial differential equations; they're going to even be of curiosity to researchers engaged on similar topics.
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