Abstract
We establish higher-order Fefferman-Poincare type inequalities with a potential belonging to an appropriate higher-order Stummel-Kato type class introduced in this paper. As an application, we obtain a priori ${L^{p}}$ estimates for solutions of higher-order elliptic equations with discontinuous coefficients of small BMO type and a potential belonging to the higher-order Stummel-Kato type class.
Highlights
1 Introduction and main results Fefferman proved in [ ] that if a potential V belonging to the classical Morrey space Lr,n– r(Rn) with < r ≤ n/, there exists a positive constant c, independent of u, such that
The result has been extended to many more general settings and applied to study Harnack’s inequality, unique continuation for nonnegative solutions and regularity of solutions of elliptic equations
Let us recall that one says V ∈ S(Rn) (n ≥ ) if V ∈ L loc(Rn), and for any r >, φV (r) := sup
Summary
Introduction and main resultsFefferman proved in [ ] that if a potential V belonging to the classical Morrey space Lr,n– r(Rn) with < r ≤ n/ , there exists a positive constant c, independent of u, such thatV (x) u(x) dx ≤ c ∇u(x) dx, u ∈ C ∞ Rn. 1 Introduction and main results Fefferman proved in [ ] that if a potential V belonging to the classical Morrey space Lr,n– r(Rn) with < r ≤ n/ , there exists a positive constant c, independent of u, such that We introduce the following higher-order Stummel-Kato type class Spm(Rn).
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