Geodesic
The First Boundary-Value Problem for Strongly Elliptic Functional-Differential Equations with Orthotropic Contractions
Matematičeskie zametki, Tome 97 (2015) no. 5, pp. 733-748

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We obtain a number of necessary and sufficient strong ellipticity conditions for a functional-differential equation containing, in its leading part, orthotropic contractions of the argument of the unknown function. We establish the unique solvability of the first boundary-value problem and the discreteness, semiboundedness, and sectorial structure of its spectrum.
Keywords: strong elliptic functional-differential equation, first boundary-value problem, orthotropic contraction, Gårding-type inequality, strong ellipticity condition, Plancherel's theorem, Riesz theorem, difference operator.
Mots-clés : Fourier transform 
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     author = {L. E. Rossovskii and A. L. Tasevich},
     title = {The {First} {Boundary-Value} {Problem} for {Strongly} {Elliptic} {Functional-Differential} {Equations} with {Orthotropic} {Contractions}},
     journal = {Matemati\v{c}eskie zametki},
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L. E. Rossovskii; A. L. Tasevich. The First Boundary-Value Problem for Strongly Elliptic Functional-Differential Equations with Orthotropic Contractions. Matematičeskie zametki, Tome 97 (2015) no. 5, pp. 733-748. http://geodesic.mathdoc.fr/item/MZM_2015_97_5_a7/