Morrey estimates for parabolic nondivergence operators of Hörmander type
Multiscale finite element coarse spaces for the application to linear elasticity
We extend the multiscale finite element method (MsFEM) as formulated by Hou and Wu in [Hou T.Y., Wu X.-H., A multiscale finite element method for elliptic problems in composite materials and porous media, J. Comput. Phys., 1997, 134(1), 169–189] to the PDE system of linear elasticity. The application, motivated by the multiscale analysis of highly heterogeneous composite materials, is twofold. Resolving the heterogeneities on the finest scale, we utilize the linear MsFEM basis for the construction...
Necessary conditions of existence for an elliptic equation with source term and measure data involving -Laplacian.
Nonlinear degenerate elliptic equations with measure data
In this paper we prove existence results for some nonlinear degenerate elliptic equations with data in the space of bounded Radon measures and we improve the results already obtained in Cirmi G.R., On the existence of solutions to non-linear degenerate elliptic equations with measure data, Ricerche Mat. 42 (1993), no. 2, 315–329.
Nonlinear equations with natural growth terms and measure data.
Nonlinear parabolic equations with natural growth terms and measure initial data
Nonlinear stability of centered rarefaction waves of the Jin-Xin relaxation model for conservation laws.
Nonuniqueness in the martingale problem and the Dirichlet problem for uniformly elliptic operators
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.