Sentence examples for form operators from inspiring English sources

We establish Dahlbergʼs perturbation theorem for non-divergence form operators L="A∇2.

Model examples are non-symmetric divergence form operators and fractional laplacians with possibly variable exponents.

The improved condition is exactly the same one as is required for divergence form operators L= divA∇.

There is a broad, more recent literature dealing with Gaussian estimates for non divergence form operators with Hölder continuous coefficients (a_{ij}).

We prove that the Lp spectrum of uniformly elliptic divergence form operators on a complete Riemannian manifold is independent of p ∈ [1, ∞] if the volume of the manifold grows uniformly subexponentially.

As a consequence we also improve a result from Dindoš et al. (2007) [4] for the Lp solvability of non-divergence form operators (Theorem 3.2) by substantially weakening the condition required on the coefficients of the operator.

We define classes determined by these indices and show that some of these classes form operator ideals.

Let be a divergence form operator with Lipschitz continuous coefficients in a domain, and let be a continuous weak solution of in.

We define the following bilinear form operator: B u,v):=Pbigl((ucdotnabla vbigr),quad forall u,v in E, (2.6) and the trilinear form operator b u,v,w =sum^{2}_{i, j=1}int _{Omega}u_{i}frac{partial v_{j}}{partial x_{i}}cdot w_{j}, dx=bigl(B u,v),wbigr).

For instance, the results apply to the Dirichlet heat kernel associated with a uniformly elliptic divergence form operator with symmetric second order part and bounded measurable real coefficients in inner uniform domains in Rn.

Gentzen had confined his study to sentence-forming operators.