## Nonlinear Partial Differential Equations and Free Boundaries: Elliptic Equations |

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A&iume 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 formulation free boundary F(u g and h Hausdorff measure instance integral iolution o& isoperimetric inequality iuch Lipschitz continuous maximal monotone graph maximum principle meas multivalued equations nondecreasing nonlinear equations nonnegative null set N(u obstacle problem obtain partial differential equations proof of Theorem Proposition proved quasilinear quasilinear equations radially symmetric recall regularity Remark resp satisfies second order Section 1.1 semilinear equation solution of 1),(2 space strong maximum principle subsection super and subsolutions supersolution symmetric rearrangement theAe Theorem 1.9 tion unique variational inequalities weak solution wheAe x e n zero order reactions