Sentence examples for extremal boundary from inspiring English sources

In this paper we shall prove that any semicontinuous affine real function, defined on a compact convex set, satisfies the boundary barycentric calculus, with respect to the measure induced on the extremal boundary of the set by any maximal Radon probability measure.

The term "variational inverse boundary-value problem" is used to designate a class of two-dimensional boundary-value problems with unknown boundaries, in which it is required to find both the solution of a partial differential equation and its domain of definition, where the latter satisfies some extremal property, and one boundary condition is specified on its boundary.

By using the method of lower and upper solutions in reversed order coupled with the monotone iterative technique, we obtain the extremal solutions of the boundary value problem.

Monotone iterative techniques to develop conditions for extremal solutions to coupled boundary value problems are very rarely studied and very few articles are devoted to this.

This paper is concerned with the existence of extremal solutions of periodic boundary value problems for second-order impulsive integro-differential equations with integral jump conditions.

In this work, the existence criteria of extremal solutions of periodic boundary value problems for the first-order dynamic equations on time scales are given by using the method of lower and upper solutions coupled with the monotone iterative technique.

We establish that sufficiently smooth solutions to the convex extremal problems with given boundary values are affine on line segments and the domain D is foliated by such segments.

The monotone iterative technique coupled with the method of upper and lower solutions has been used to study the existence of extremal solutions of periodic boundary value problems for second-order impulsive equations; see, for example, [36 41].

In this paper, we establish the existence and uniqueness of extremal solutions for nonlinear boundary value problems of a singular fractional p-Laplacian differential equation involving Riemann-Liouville derivatives.

However, there are few papers to deal with the existence for the extremal solutions to periodic boundary value problems of first order dynamic equations on time scales based on the method of lower and upper solutions coupled with monotone iterative technique under these two cases.

In this talk we will give an overview of progress that has been made on an eigenvalue extremal problem for surfaces with boundary, and contrast this with recent results in higher dimensions.