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Elliptic functional differential equations with degenerations. (English) Zbl 1471.35291
Summary: This review is devoted to differential-difference equations with degeneration in a bounded domain \(Q\subset\mathbb{R}^n\) and applications (Kato conjecture, nonlocal boundary value problem). We consider differential-difference operators with degeneration of the second order and generalization to \(2m\)-order and the case where differential-difference operator contains several degenerate difference operators with degeneration. Generalized solutions of such equations may not belong even to the Sobolev space \(W^1_2(Q)\).
MSC:
35R10 Partial functional-differential equations
35J25 Boundary value problems for second-order elliptic equations
39A14 Partial difference equations
39A27 Boundary value problems for difference equations
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