## Free Boundary Problems: Applications and Theory, Volume 1 |

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### Contents

INTR0DUCTI0N 1 | 16 |

linear diffusion term | 86 |

EXISTENCE AND L0CATI0N 0F THE FREE B0UNDARY BY MEANS | 212 |

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a.e. x e applied assume assumption ball Banach Banach space boundary conditions Brezis Cauchy problem Chapter coincidence set compact support comparison principle consider constant continuou& convex function convex set deduce defined Diaz differential inequality diffusion Dirichlet Dirichlet problem elliptic equations energy method estimate eveAy Finally free boundary F(u g and h Hausdorff measure instance integral iolution o& iome isoperimetric inequality iuch Let u e linear Lipschitz continuous Lp(ft Lp(G maximal monotone graph maximum principle meas MoieoveA nondecreasing nonlinear equations nonnegative null set N(u obstacle problem obtain p(ft partial differential equations proof of Theorem Proposition proved quasilinear quasilinear equations radially symmetric recall Remark resp satisfies second order Section 1.1 semilinear equation solution of 1),(2 space strong maximum principle subsection super and subsolutions supersolution theAe Theorem 1.9 tion unique variational inequalities wheAe zero order reactions