Positivity of two-dimensional elliptic differential operators in Ho¨lder spaces.

This paper considers the operator Au(t,x) = -a 11 (t,x)u tt (t,x)-a 22 (t,x)u xx (t,x)+σu(t,x) , defined over the region R + ×R with the boundary condition u(0,x) = 0,x∈R. Here, the coefficients aii(t,x), i = 1,2 are continuously differentiable and satisfy the uniform ellipticity condition a 11 2 (t,x)+a 22 2 (t,x)≥δ>0 , and σ > 0. It investigates the structure of the fractional spaces generated by this operator. Moreover, the positivity of the operator in Ho¨lder spaces is proved. [ABSTRACT FROM AUTHOR]

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