Smooth solutions to a class of free boundary parabolic problems

On the existence of nonnegative solutions for a class of fractional boundary value problems

‎In this paper‎, ‎we provide sufficient conditions for the existence of nonnegative solutions of a boundary value problem for a fractional order differential equation‎. ‎By applying Kranoselskii`s fixed--point theorem in a cone‎, ‎first we prove the existence of solutions of an auxiliary BVP formulated by truncating the response function‎. ‎Then the Arzela--Ascoli theorem is used to take $C^1$ ...

Variational Modeling of Parabolic Free Boundary Problems

INFINITELY MANY SOLUTIONS FOR A CLASS OF P-BIHARMONIC PROBLEMS WITH NEUMANN BOUNDARY CONDITIONS

The existence of infinitely many solutions is established for a class of nonlinear functionals involving the p-biharmonic operator with nonhomoge- neous Neumann boundary conditions. Using a recent critical-point theorem for nonsmooth functionals and under appropriate behavior of the nonlinear term and nonhomogeneous Neumann boundary conditions, we obtain the result.

Free Boundary Problems for Parabolic Equations

An address delivered at the Ann Arbor meeting of the American Mathematical Society on November 29, 1969, by invitation of the Committee to Select Hour Speakers for Western Sectional Meetings; received by the editors April 9,1969. AMS 1969 subject classifications. Primary 3562, 3578.

A General Class of Free Boundary Problems for Fully Nonlinear Parabolic Equations

In this paper we consider the fully nonlinear parabolic free boundary problem { F (Du)− ∂tu = 1 a.e. in Q1 ∩ Ω |Du|+ |∂tu| ≤ K a.e. in Q1 \ Ω, where K > 0 is a positive constant, and Ω is an (unknown) open set. Our main result is the optimal regularity for solutions to this problem: namely, we prove that W 2,n x ∩W 1,n t solutions are locally C 1,1 x ∩C 0,1 t inside Q1. A key starting point for...