Oblique derivative problems in Lipschitz domains: II. Discontinuous boundary data.
On a boundary value problem for an equation of the type of non-stationary filtration
On a nonlinear degenerate parabolic transport-diffusion equation with a discontinuous coefficient.
On some boundary value problems for one mixed equation with discontinuous coefficients in a rectangular domain.
On some elliptic transmission problems
Boundary value problems for second order linear elliptic equations with coefficients having discontinuities of the first kind on an infinite number of smooth surfaces are studied. Existence, uniqueness and regularity results are furnished for the diffraction problem in such a bounded domain, and for the corresponding transmission problem in all of . The transmission problem corresponding to the scattering of acoustic plane waves by an infinitely stratified scatterer, consisting of layers with physically...
On some -estimates for solutions of elliptic equations in unbounded domains
In this review article we present an overview on some a priori estimates in , , recently obtained in the framework of the study of a certain kind of Dirichlet problem in unbounded domains. More precisely, we consider a linear uniformly elliptic second order differential operator in divergence form with bounded leading coeffcients and with lower order terms coefficients belonging to certain Morrey type spaces. Under suitable assumptions on the data, we first show two -bounds, , for the solution...
On the approximation of elliptic operators with discontinuous coefficients
On the Cauchy problem for the equation of one-dimensional non-stationary filtration with non-continuous initial data
On the interior smoothness of solutions to second-order elliptic equations.
On the parabolic potentials in degenerate-type heat equation.
On the regularity of solutions of a thermoelastic system under noncontinuous heating regimes. III
In this part we weaken the sufficient condition to obtain the stresses continuous and bounded in the threedimensional case, and we treat a certain coupled system.
On the regularity of solutions of a thermoelastic system under noncontinuous heating regimes
The continuity and boundedness of the stress to the solution of the thermoelastic system is studied first for the linear case on a strip and then for the twodimensional model involving nonlinearities, noncontinuous heating regimes and isolated boundary nonsmoothnesses of the heated body.
On the regularity of solutions of a thermoelastic system under noncontinuous heating regimes. II
A quasilinear noncoupled thermoelastic system is studied both on a threedimensional bounded domain with a smooth boundary and for a generalized model involving the influence of supports. Sufficient conditions are derived under which the stresses are bounded and continuous on the closure of the domain.
On the solution of reaction-diffusion equations with double diffusivity.
On the uniqueness problem for quasilinear elliptic equations involving measures.
We discuss the uniqueness of solutions to problems like⎧ λ |u|s-1u - div (|∇u|p-2∇u) = μ on Ω,⎨⎩ u = 0 in ∂Ω,where λ ≥ 0 and μ is a signed Radon measure.
On the -regularity of solutions to systems of differential equations in the case when the equations are constructed from discontinuous functions.
On the well posedness of a system of balance laws with data
On time-harmonic Maxwell equations with nonhomogeneous conductivities: Solvability and FE-approximation
The solvability of time-harmonic Maxwell equations in the 3D-case with nonhomogeneous conductivities is considered by adapting Sobolev space technique and variational formulation of the problem in question. Moreover, a finite element approximation is presented in the 3D-case together with an error estimate in the energy norm. Some remarks are given to the 2D-problem arising from geophysics.
On two-dimensional hamiltonian transport equations with Llocp coefficients
On unique solvability of the periodic problem in the plane for linear hyperbolic equations.