For fermionic fields on a compact Riemannian manifold with boundary one has a choice between local and non-local (spectral) boundary conditions. The one-loop prefactor in the Hartle-Hawking amplitude in quantum cosmology can then be studied using the generalized Riemann ζ-function formed from the squared eigenvalues of the four-dimensional fermionic operators. For a massless Majorana spin2 fiel...

On linear ODEs with a time singularity of the rst kind and unsmooth inhomo-geneity 6/2014 A degenerate fourth-order parabolic equation modeling Bose-Einstein condensation. We consider the symmetric FEM-BEM coupling that connects two linear elliptic second order partial differential equations posed in a bounded domain Ω and its complement, where the exterior problem is restated by an integral eq...

this study concerns the existence and multiplicity of positive weak solutions for a class ofsemilinear elliptic systems with nonlinear boundary conditions. our results is depending onthe local minimization method on the nehari manifold and some variational techniques. alsoby using mountain pass lemma, we establish the existence of at least one solution withpositive energy.

(1)  ut −∆u = f in Ω× (0, T ), u = 0 on ∂Ω× (0, T ), u(·, 0) = u0 in Ω. Here u = u(x, t) is a function of spatial variable x ∈ Ω and time variable t ∈ (0, T ). The Laplace differential operator ∆ is taking with respect to the spatial variable. For the simplicity of exposition, we consider only homogenous Dirichlet boundary condition and comment on the adaptation to Neumann and other type of b...