Representation formulae for nonhomogeneous differential operators and applications to PDEs
Lorenzo D’Ambrosio, Marius Ghergu
Abstract
We obtain integral representation formulae for functions u∈Lloc1(RN) which satisfy P(−Δ)u=μ in the sense of distributions in RN, where μ is a positive Radon measure on RN and P(z)=zm(zσ+aσ−1zσ−1+⋯+a1z+a0) is a nonconstant real polynomial whose roots belong to the interval (−∞,0], m,σ≥0, N>2m. Further, we apply these results to a number of nonhomogeneous higher order differential inequalities.
Topics & Concepts
MathematicsRepresentation (politics)Order (exchange)Interval (graph theory)Differential operatorPolynomialPure mathematicsMeasure (data warehouse)Differential (mechanical device)Discrete mathematicsMathematical analysisCombinatoricsAerospace engineeringLawPolitical scienceEngineeringComputer scienceFinanceDatabaseEconomicsPoliticsMathematical functions and polynomialsNumerical methods in inverse problemsDifferential Equations and Boundary Problems