## Nonlinear Partial Differential Equations with ApplicationsThis book primarily concerns quasilinear and semilinear elliptic and parabolic partial differential equations, inequalities, and systems. The exposition quickly leads general theory to analysis of concrete equations, which have specific applications in such areas as electrically (semi-) conductive media, modeling of biological systems, and mechanical engineering. Methods of Galerkin or of Rothe are exposed in a large generality. |

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### Contents

1 | |

Pseudomonotone or weakly continuous mappings 29 | 28 |

Accretive mappings | 89 |

smooth case | 109 |

Nonsmooth problems variational inequalities | 125 |

Implicit variational problems and quasivariational inequalities | 156 |

particular examples | 161 |

Special auxiliary tools | 187 |

On elliptic partial differential equations Ann Scuola | 265 |

Evolution governed by accretive mappings | 275 |

Evolution governed by certain setvalued mappings 305 | 304 |

Doublynonlinear problems | 321 |

99 | 346 |

particular examples | 357 |

383 | |

399 | |

Evolution by pseudomonotone or weakly continuous mappings 199 | 198 |

252 Moser J A new proof of De Giorgis theorem concerning the regularity problem | 252 |

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a-priori estimates a.a. t e a.e. in Q A(uk accretive approximation assume assumption Aubin-Lions Banach space boundary conditions bounded coercive compact compact embedding consider convergence convex defined denotes dense derivative differential Dirichlet Dirichlet boundary conditions dom(A dom(L embedding equation Example Exercise follows formula function Galerkin Galerkin method Green's formula Gronwall inequality growth condition hence Hint Hölder's Hölder's inequality holds implies Lebesgue Lemma limit passage linear Lipschitz continuous Lº Q Lº(Q locally convex space Lºº lower semicontinuous LP Q LP(I LP(Q m-accretive modify monotone Moreover Nemytskii mapping nonlinear norm obtain Proposition prove pseudomonotone radially continuous realize Remark satisfy sequence set-valued ſº Sobolev space strong solution subsequence term uniformly unique variational inequality weak formulation weak solution weakly continuous WºO