Elliptic and Parabolic Equations with Discontinuous Coefficients

By A. Maugeri, D. Palagachev, Lubomira G. Softova. 2000

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Parabolic Equations with Measurable Coefficients (2006, background): “It is worth noting that after [2], [3], [1] there were very many publications on elliptic and parabolic equations with VMO coefficients (see, for instance, the above mentioned references and [5], [12], [13], [14], [15], and many references therein).”
A mostly elementary proof of Morrey space estimates for elliptic and parabolic equations with VMO coefficients (2003, background): “8 of [25] as a Cordes condition for the boundary operator arises.”
The dirichlet problem in lipschitz domains for higher order elliptic systems with rough coefficients (2007, unknown): “For each y′ ∈ Rn−1 we introduce the Poisson matrices P0, . . . , Pm−1 for the problem (2.4), i.e., the solutions of the boundary-value problems L(Dx)Pj(x, y ′) = 0 Il in R n +, ( ∂k ∂xkn Pj ) ( (x′, 0), y′ ) = δjk δ(x ′ − y′)Il for x ′ ∈ Rn−1, 0 ≤ k ≤ m− 1, (2.5) where δjk is the usual…”
On the Lp-Solvability of Higher Order Parabolic and Elliptic Systems with BMO Coefficients (2010, background): “For further related results, we refer the reader to the book [31] and reference therein.”