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Ll(JR n ). 26). One has (e- 2 ;S(Ko+V))(x,v)V(v)(po(1 ~I + 3 + k,v,y) - Po (1 + 3,V,y))1 2 1 }2 dx { I dv I dv ' IItn iR n JRn 1 (Po(2 + 23 + 2k, v, Vi) - 2Po(2 + 23 + k, v, Vi) + Po(2 + 23, v, Vi)) } "2.

Partial Differential Equations (to appear). : Coefficients des Singularites pour des problemes aux limites elliptiques sur une Domaine a Points coniques I: Resultats generaux pour Ie probleme de Dirichlet; RAIRO Model. Math. Anal. Numer. 24 (1990), 27-52. F. Ali Mehmeti and S. : Elliptic problems in nonsmooth Domains; Monographs and Studies in Mathematics 21, Pitman, Boston 1985. : Boundary value problems for elliptic equations in domains with conical or angular points; Trans. Moscow Math. Soc.

Rn J. van Casteren and M. Demuth 42 Now we are able to formulate the results in this note. 1. n) given by po(t,:r,y). Assume that Po satisfies BASSA. Moreover we assume that e- tKo is £1 - L OO smoothing, i. 14) sup Po(t,x,y) < 00. n \ r be the complement of r. , KE is the operator corresponding to Ko with Dirichlet boundary condition on ar. ~ s~p dy Po(s, x, y) I V(y) I = O. n). Correspondingly we denote by (KO+V)E the Friedrichs extension of Ko + Vt[dom (Ko + V) nL2(~)1. 17) [a+V(X(u))]du dxE x e O , Tr < } 00 < 00, IR n where a > 0 is chosen large enough.

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Control and Estimation of Distributed Parameter Systems by W. Desch, F. Kappel, K. Kunisch


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