## Advances in Mathematical Sciences and Applications, Volume 7, Pages 525-1010 |

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Advances in Mathematical Appl Applications Gakkotosho apply approximation assume assumptions asymptotic Banach space behaviour bifurcation boundary conditions boundary value problems Cauchy problem coefficients compact convex Corollary deduce defined definition denote density depending differential equations elliptic finite element finite element method fixed function given Hardy space Harnack inequality Heisenberg group Hence holds homogeneous Hormander implies infinity initial boundary value initial data integral Krasnosel'skij liminf linear operators Math Mathematical Sciences maximum principle method Moreover nonlinear nonnegative norm notation obtain parabolic parameter positive constant positive solution proof of Theorem properties Proposition prove rapidly decaying solution regularity Remark resp respect satisfies Sciences and Applications semigroup sequence shape memory alloys singular smooth Sobolev spaces solution of 0.1 Stefan problems term Theorem 1.1 uniformly unique solution variational inequality vector fields weak solution weakly