## Nonlinear analysis and continuum mechanics: papers for the 65th birthday of James SerrinThe chapters in this volume deal with four fields with deep historical roots that remain active areas reasearch: partial differential equations, variational methods, fluid mechanics, and thermodynamics. The collection is intended to serve two purposes: First, to honor James Serrin, in whose work the four fields frequently interacted; and second, to bring together work in fields that are usually pursued independently but that remain remarkably interrelated. Serrin's contributions to mathematical analysis and its applications are fundamental and include such theorems and methods as the Gilbarg- Serrin theorem on isoated singularities, the Serrin symmetry theorem, the Alexandrov-Serrin moving-plane technique, The Peletier-Serrin uniqueness theorem, and the Serrin integal of the calculus of variations. Serrin has also been noted for the elegance of his mathematical work and for the effectiveness of his teaching and collaborations. |

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### Contents

Invariance and Balance in Continuum Mechanics | 27 |

Some Regularity Properties of Locally Weakly Invertible Maps | 45 |

Some Recent Results on SaintVenants Principle | 61 |

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Amer Anal analysis Appl approximation numbers Arch asymptotic behavior asymptotic stability Barenblatt boundary conditions boundary value problem calculus of variations Cauchy classical coefficients compact continuous Continuum Mechanics cos(l dB(a defined denote Dirichlet Dirichlet problem eigenvalue elasticity elliptic equations embeddings energy entropy numbers estimates existence finite fluid follows frame free boundary problems Friedrichs inequalities function Giaquinta global hence inequality Int(A integral James Serrin L.A. Peletier Ladyzhenskaya Lebesgue Lemma linear maps mean curvature Modica Navier-Stokes equations nonlinear diffusion norm paper Partial Differential Equations periodic solutions Poincare positive solution Proc Professor Serrin proof properties proved Pucci quasi-linear elliptic Rational Mech Saint-Venant's principle satisfies self-similar self-similar solutions semigroup sin2 singular Sobolev Sobolev space solutions of elliptic Soucek space Springer-Verlag subbodies Suppose symmetric tensor Theorem 7.1 theory thermodynamics Triebel turbulent bursts University of Ferrara vector velocity