Spectral Theory of Singular Elliptic Operators with Measurable Coefficients

We study higher order elliptic operators with measurable coefficients acting on Euclidean domains. The coefficients may have degeneracies or singularities on the boundary or at infinity. We prove Gaussian-type bounds on the fundamental solution of the associated semigroup. These bounds are expressed in terms of a distanced(x, y) that reflects the singularity or degeneracy of the coefficients. The estimates are then used to extend the semigroup to otherLpspaces and to prove that theLp-spectrum isp-independent.