Coerciveness of functional-differential equations
Matematičeskie zametki, Tome 59 (1996) no. 1, pp. 103-113.

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We consider functional-differential equations with the Dirichlet conditions and with contraction and dilatation of the arguments. Necessary and sufficient conditions are obtained under which a Garding type inequality holds. These results allow us to verify coerciveness by using a special “symbol” of the equation considered.
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L. E. Rossovskii. Coerciveness of functional-differential equations. Matematičeskie zametki, Tome 59 (1996) no. 1, pp. 103-113. http://geodesic.mathdoc.fr/item/MZM_1996_59_1_a9/

[1] Vishik M. I., “O silno ellipticheskikh sistemakh differentsialnykh uravnenii”, Matem. sb., 29:3 (1951), 615–676 | MR | Zbl

[2] Gårding L., “Dirichlet's problem for linear elliptic partial differential equations”, Math. Scand., 1:1 (1953), 55–72 | MR

[3] Agmon S., “The coerciveness problem for integro-differential forms”, J. Analyse Math., 6:1 (1958), 183–223 | DOI | MR | Zbl

[4] Figueiredo D. G., “The coerciveness problem for forms over vector-valued functions”, Comm. Pure Appl. Math., 16:1 (1963), 63–94 | DOI | MR | Zbl

[5] Necas J., “Sur les normes équivalentes dans $W_p^{(k)}(\Omega)$ et sur la coercivité des formes formellement positives”, Sémin. de Math. Super., Montréal, 1965

[6] Skubachevskii A., “The first boundary value problem for strongly elliptic differential-difference equations”, J. Diff. Equat., 63:3 (1986), 332–361 | DOI | MR

[7] Rudin U., Funktsionalnyi analiz, Mir, M., 1975