A Dirichlet Problem with Free Gradient Discontinuity

Gradient Bounds for Minimizers of Free Discontinuity Problems Related to Cohesive Zone Models in Fracture Mechanics

In this note we consider a free discontinuity problem for a scalar function, whose energy depends also on the size of the jump. We prove that the gradient of every smooth local minimizer never exceeds a constant, determined only by the data of the problem.

Second Order Variational Problems with Free Discontinuity and Free Gradient Discontinuity

A Simple and Systematic Approach for Implementing Boundary Conditions in the Differential Quadrature Free and Forced Vibration Analysis of Beams and Rectangular Plates

This paper presents a simple and systematic way for imposing boundary conditions in the differential quadrature free and forced vibration analysis of beams and rectangular plates. First, the Dirichlet- and Neumann-type boundary conditions of the beam (or plate) are expressed as differential quadrature analog equations at the grid points on or near the boundaries. Then, similar to CBCGE (direct ...

Existence Results for a Dirichlet Quasilinear Elliptic Problem

In this paper, existence results of positive classical solutions for a class of second-order differential equations with the nonlinearity dependent on the derivative are established. The approach is based on variational methods.

Iterative Thresholding Meets Free-Discontinuity Problems

Free-discontinuity problems describe situations where the solution of interest is defined by a function and a lower dimensional set consisting of the discontinuities of the function. Hence, the derivative of the solution is assumed to be a ‘small’ function almost everywhere except on sets where it concentrates as a singular measure. This is the case, for instance, in crack detection from fractu...