We introduce explicit and exact variational formulations for the weakly singular and hypersingular operators over an open interval as well as for their corresponding inverses. Contrary to the case of a closed curve, these ...

This paper concerns with the heat equation in the half-space ℝ+n with nonlinearity and singular potential on the boundary ∂ℝ+n. We show a well-posedness result that allows us to consider critical potentials with infinite ...

We prove convergence and quasi-optimality of a lowest-order adaptive boundary element method for a weakly-singular integral equation in 2D. The adaptive mesh-refinement is driven by the weighted-residual error estimator. ...

In this paper we deal with the stability of solutions to fractional p-Laplace problems with nonlinear sources when the fractional parameter s goes to 1. We prove a general convergence result for general weak solutions which ...