Three-dimensional mathematical problems of the elasticity theory of anisotropic piecewise homogeneous bodies are discussed. A mixed type boundary contact problem is considered where on one part of the interface, rigid contact conditions are given (jumps of the displacement and the stress vectors are known), while on the remaining part screen or crack type boundary conditions are imposed. The in...

We propose to study a fully nonlinear version of the Yamabe problem on manifolds with boundary. The boundary condition for the conformal metric is the mean curvature. We establish some Liouville type theorems and Harnack type inequalities.

In this paper we consider 2D nonlocal diffusion models with a finite horizon parameter δ characterizing the range of interactions, and treatment Neumann-like boundary conditions that have proven challenging for discretizations models. We propose new generalization classical local Neumann by converting flux to correction term in model, which provides an estimate interactions each point points ou...