The interior gradient estimate of Hessian quotient equations

Universal estimate of the gradient for parabolic equations

We suggest a modification of the estimate for weighted L2-norm of the solution gradient of a parabolic equation via L2-norm of the free term. We found the limit upper estimate that can be achieved by transformation of the equation via adding a constant to the zero order coefficient. This upper limit estimate is used to obtain an asymptotic estimate for this weighted norm of the gradient at init...

Interior estimate on the space

Abstract. We will prove an interior estimate for the mappings on the space, which is generalization of the Heinz-Bernstein theorem for the plane. In other worlds we prove the theorem. Let s : Bn → R (s : Bn → Bm) be a continuous function from the closed unit ball Bn ⊂ R into the real line (closed unit ball in R) satisfying the conditions: (i) s is C on U, (ii) s is C in ∂B = Sn−1 and (iii) |∆s|...

Research Article Interior Gradient Estimates for Nonuniformly Parabolic Equations II

Page 1 INTERIOR GRADIENT ESTIMATES FOR MEAN CURVATURE EQUATIONS

In this paper we give a simple proof for the interior gradient estimate for curvature and Hessian equations. We also derive a Liouville type result for these equations. §0. Introduction The interior gradient estimate for the prescribed mean curvature equation has been extensively studied, see [9] and the references therein. For high order mean curvature equations it has also been obtained in [1...

Quotient Structure of Interior-closure Texture Spaces

In this paper, we consider quotient structure and quotient difunctions in the context of interior and closure operators on textures in the sense of Dikranjan-Giuli. The generalizations of several results concerning separation and quotient mapping are presented. It is shown that the category of interior-closure spaces and bicontinuous difunctions has a T0 reflection. Finally, we introduce some c...