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تسجيل مستخدم جديدExistence and Spectral Theory for Weak Solutions of Neumann and Dirichlet Problems for Linear Degenerate Elliptic Operators with Rough Coefficients
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In this paper we study existence and spectral properties for weak solutions of Neumann and Dirichlet problems associated to second order linear degenerate elliptic partial differential operators $X$, with rough coefficients of the form $$X=-text{div}(P abla )+{bf HR}+{bf S^prime G} +F$$ in a geometric homogeneous space setting where the $ntimes n$ matrix function $P=P(x)$ is allowed to degenerate. We give a maximum principle for weak solutions of $Xuleq 0$ and follow this with a result describing a relationship between compact projection of the degenerate Sobolev space $QH^{1,p}$ into $L^q$ and a Poincare inequality with gain adapted to $Q$.
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This article gives an existence theory for weak solutions of second order non-elliptic linear Dirichlet problems of the form {eqnarray} ablaP(x) abla u +{bf HR}u+{bf SG}u +Fu &=& f+{bf Tg} textrm{in}Theta u&=&phitextrm{on}partial Theta.{eqnarray} Th
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