Wavelet–Galerkin solutions of one dimensional elliptic problems

On the Determinant of One-Dimensional Elliptic Boundary Value Problems

We discuss the ζ−regularized determinant of elliptic boundary value problems on a line segment. Our framework is applicable for separated and non-separated boundary conditions.

Generalized Solutions of Nonlocal Elliptic Problems

An elliptic equation of order 2m with general nonlocal boundary-value conditions, in a plane bounded domain G with piecewise smooth boundary, is considered. Generalized solutions belonging to the Sobolev space Wm 2 (G) are studied. The Fredholm property of the unbounded operator corresponding to the elliptic equation, acting on L2(G), and defined for functions from the space Wm 2 (G) that satis...

Regularity of solutions to one-dimensional and multi-dimensional problems in the calculus of variations

Viscosity solutions for elliptic-parabolic problems

We study an elliptic-parabolic problem appearing in the theory of partially saturated flows in the framework of viscosity solutions. This is part of current investigation to understand the theory of viscosity solutions for PDE problems involving free boundaries. We prove that the problem is well posed in the viscosity setting and compare the results with the weak theory. Dirichlet or Neumann bo...

Uniqueness of Entropy Solutions of Nonlinear Elliptic-Parabolic-Hyperbolic Problems in One Dimension Space

We consider a class of elliptic-parabolic-hyperbolic degenerate equations of the form b(u)t−a(u, φ(u)x)x = f with homogeneous Dirichlet conditions and initial conditions. In this paper we prove an L-contraction principle and the uniqueness of entropy solutions under rather general assumptions on the data.