## Introduction to the theory of nonlinear elliptic equations |

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### Contents

The topic of the lecture notes and something on modelling | 9 |

Sobolev and MorreyCampanato spaces | 21 |

Existence of weak solutions to boundary value problems | 36 |

Copyright | |

4 other sections not shown

### Common terms and phrases

absolutely continuous ar(x ari(x Banach space bounded domain bounded function BR(x coefficients coercive completely continuous conditions of Theorem continuous function continuously differentiable convex defined DEFINITION demicontinuous denote DF(u diffeomorphism Dirichlet problem dxi dxj elliptic systems estimate everywhere in Q example Fatou's lemma finite elasticity follows G(un Galerkin method growth conditions hence Hilbert space homeomorphism hr(x implies inequality lecture notes Lemma let F Let Q Let the conditions Let u e Let us consider Let us remark Let us suppose lim T(un linear Lipschitz boundary Lipschitz continuous mapping Necas nonlinear notation once continuously differentiable polynomial proof of Theorem prove pseudomonotony reader result sake of simplicity satisfies the condition scalar product Sobolev spaces sup u(x tensor tion un+1 Vw(x w e Ker weak solution weakly wr(x