Counting dimensions of L - harmonic functions
نویسندگان
چکیده
In this article, we will consider second order uniformly elliptic operators of divergence form defined on Rn with measurable coefficients. Mainly, we will give estimates on the dimension of space of solutions that grow at most polynomially of degree d. More precisely, in terms of a rectangular coordinate system {x1, . . . , xn}, a second order uniformly elliptic operator of divergence form, L, acting on a function f ∈ H1 loc(R) is given by
منابع مشابه
To appear in J.Diff.Geom. COUNTING MASSIVE SETS AND DIMENSIONS OF HARMONIC FUNCTIONS
In a previous article of the authors [L-W1], they introduced the notion of dmassive sets. Using this, they proved a structural theorem for polynomial growth harmonic maps into a Cartan-Hadamard manifold with strongly negative sectional curvature. When d = 0, the maximum number of disjoint 0-massive sets m0(M) admissible on a complete manifold M is known [G] to be the same as the dimension h0(M)...
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