Anisotropic nonlinear elliptic systems with measure data and anisotropic harmonic maps into spheres.
Another approach to vibration analysis of stepped structures.
Approche visqueuse de solutions discontinues de systèmes hyperboliques semilinéaires
On s’intéresse à des systèmes symétriques hyperboliques multidimensionnels en présence d’une semilinéarité. Il est bien connu que ces systèmes admettent des solutions discontinues, régulières de part et d’autre d’une hypersurface lisse caractéristique de multiplicité constante. Une telle solution étant donnée, on montre que est limite quand de solutions du système perturbé par une viscosité de taille . La preuve utilise un problème mixte parabolique et des développements de couches limites....
Approximation of singularly perturbed parabolic reaction-diffusion equations with nonsmooth data.
for parabolic measures
If Ω is a Lip(1,1/2) domain, μ a doubling measure on , i = 0,1, are two parabolic-type operators with coefficients bounded and measurable, 2 ≤ q < ∞, then the associated measures , have the property that implies is absolutely continuous with respect to whenever a certain Carleson-type condition holds on the difference function of the coefficients of and . Also implies whenever both measures are center-doubling measures. This is B. Dahlberg’s result for elliptic measures extended...
BMO continuity for some heat potentials
Boundary value problems in weighted spaces
Capacitary estimates of positive solutions of semilinear elliptic equations with absorbtion
Let be a bounded domain of class in N and let be a compact subset of . Assume that and denote by the maximal solution of in which vanishes on . We obtain sharp upper and lower estimates for in terms of the Bessel capacity and prove that is -moderate. In addition we describe the precise asymptotic behavior of at points , which depends on the “density” of at , measured in terms of the capacity .
Cauchy-Neumann problem for a kind of nonlinear parabolic operators.
Classical solutions of the perturbed wave equation with singular potential.
Classical solutions to the scalar conservation law with discontinuous initial data
Sufficient and necessary conditions for the existence and uniqueness of classical solutions to the Cauchy problem for the scalar conservation law are found in the class of discontinuous initial data and non-convex flux function. Regularity of rarefaction waves starting from discontinuous initial data and their dependence on the flux function are investigated and illustrated in a few examples.
Conditions aux limites non homogènes pour des problèmes elliptiques avec second membre mesure
Continuous dependence in for discontinuous solutions of the viscous -system
Corrigendum to: parabolic oblique derivative problem with discontinuous coefficients in generalized weighted Morrey spaces
Degenerate elliptic equations with measure data and nonlinear potentials
Dirichlet problem. Characterization of regularity.
Discontinuous elliptic problems in without monotonicity assumptions
We prove existence of a positive, radial solution for a semilinear elliptic problem with a discontinuous nonlinearity. We use an approximating argument which requires no monotonicity assumptions on the nonlinearity.
Discontinuous quasilinear elliptic problems at resonance
In this paper we study a quasilinear resonant problem with discontinuous right hand side. To develop an existence theory we pass to a multivalued version of the problem, by filling in the gaps at the discontinuity points. We prove the existence of a nontrivial solution using a variational approach based on the critical point theory of nonsmooth locally Lipschitz functionals.
Eliptické parciální diferenciální rovnice s degenerovanými koeficienty
Elliptic boundary problems on spaces with conic points