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.
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.
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.
We obtain the global weighted Morrey-type regularity of the solution of the regular oblique derivative problem for linear uniformly parabolic operators with VMO coefficients. We show that if the right-hand side of the parabolic equation belongs to certain generalized weighted Morrey space Mp,ϕ(Q, w), than the strong solution belongs to the generalized weighted Sobolev- Morrey space [...] W˙2,1p,φ(Q,ω).
Let be a weak solution of a quasilinear elliptic equation of the growth with a measure right hand term . We estimate at an interior point of the domain , or an irregular boundary point , in terms of a norm of , a nonlinear potential of and the Wiener integral of . This quantifies the result on necessity of the Wiener criterion.
Ce travail est consacré à l’étude du problème mixte linéaire pour un système non caractéristique, strictement hyperbolique, de degré 1, dans le cas où la condition aux limites présente un saut sur une hypersurface non caractéristique du bord. Sous la condition de Lopatinski uniforme hors de cette hypersurface et sous une hypothèse supplémentaire le long de celle-ci, on prouve un résultat d’existence et d’unicité dans l’espace de Sobolev . On étudie ensuite la propagation de la régularité conormale...