## Convexity and differential inequalities in Hilbert space |

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### Contents

CHAPTER 0 PRELIMINARIES | 6 |

CHAPTER I FIRST ORDER DIFFERENTIAL INEQUALITIES | 15 |

CHAPTER II SECOND ORDER DIFFERENTIAL INEQUALITIES | 48 |

4 other sections not shown

### Common terms and phrases

Agmon and Nirenberg analogue arguments arithmetic-geometric mean backward Cauchy problem backward problem bound for g(t boundary value problem Cauchy data Chapter coefficient consider convexity Corollary denote differential inequalities estimate example exp(ar f u:Mu)ds f)ds finite following theorem ft ft ft rt given constants heat equation Hilbert space hypotheses of Theorem Hypothesis I-C I-AQ II-A III-B ij nxn initial boundary value inner product integral interval 0,T last term Let F linear operators Moreover Mu,t Mu,tt negative semi-definite non-negative positive computable constants positive constant positive definite positive semi-definite preceding hypotheses preceding proofs prescribed proof of Theorem prove question of uniqueness Rayleigh quotient remark right hand side rt rt satisfies 5.44 satisfies the hypotheses simply skew symmetric stability suppose taking values Theorem 1.1 u:Mu u:Mu)dsj u:Nu uniqueness theorems w:Mw w:Mw)ds w:Nw well-posed problem x:Mx zero solution