This paper is concerned with the Bernstein estimates of viscosity solutions of the Cauchy problems for linear parabolic equations. The techniques of viscosity solution method given by H.Ishii and P.L. Lions in [1] all...This paper is concerned with the Bernstein estimates of viscosity solutions of the Cauchy problems for linear parabolic equations. The techniques of viscosity solution method given by H.Ishii and P.L. Lions in [1] allow us to deduce the estimates without differentiating the equation,which is in a way completely different from the classical one. We mainly get the estimate of under the corresponding assumptions on the smoothness of solutions and the known functions in the equation.展开更多
This paper discussed an axially symmetric elastic-plastic torsion problem. In virtue of penalty method, reflection boundaries, Bernstein estimate and reverse Holder inequality, on account of studying the corresponding...This paper discussed an axially symmetric elastic-plastic torsion problem. In virtue of penalty method, reflection boundaries, Bernstein estimate and reverse Holder inequality, on account of studying the corresponding complementary boundary problem which had mixed boundary conditions, the regularity of the solutions was established.展开更多
文摘This paper is concerned with the Bernstein estimates of viscosity solutions of the Cauchy problems for linear parabolic equations. The techniques of viscosity solution method given by H.Ishii and P.L. Lions in [1] allow us to deduce the estimates without differentiating the equation,which is in a way completely different from the classical one. We mainly get the estimate of under the corresponding assumptions on the smoothness of solutions and the known functions in the equation.
文摘This paper discussed an axially symmetric elastic-plastic torsion problem. In virtue of penalty method, reflection boundaries, Bernstein estimate and reverse Holder inequality, on account of studying the corresponding complementary boundary problem which had mixed boundary conditions, the regularity of the solutions was established.
