Existence of solutions of nonlinear elliptic equations with measure data in Musielak-Orlicz spaces
A. P. Kashnikova, Л. М. Кожевникова
Abstract
Abstract A second-order quasilinear elliptic equation with a measure of special form on the right-hand side is considered. Restrictions on the structure of the equation are imposed in terms of a generalized -function such that the conjugate function obeys the -condition and the corresponding Musielak-Orlicz space is not necessarily reflexive. In an arbitrary domain satisfying the segment property, the existence of an entropy solution of the Dirichlet problem is proved. It is established that this solution is renormalized. Bibliography: 29 titles.
Topics & Concepts
MathematicsMathematical analysisMeasure (data warehouse)Nonlinear systemPure mathematicsOrder (exchange)Dirichlet distributionBoundary value problemPhysicsDatabaseComputer scienceQuantum mechanicsEconomicsFinanceAdvanced Mathematical Modeling in EngineeringDifferential Equations and Boundary ProblemsNonlinear Partial Differential Equations