Parabolic PDEs with variable coefficients: uniqueness

Abstract

In this chapter we consider elliptic-parabolic equations with variable coefficients of the form

$$ L_a u: = Lu - au = 0, $$

(6.1)

where L is the second order operator

$$ L = \frac{1} {2}\sum\limits_{j,k = 1}^N {c_{jk} \partial _{x_j x_k } + } \sum\limits_{j = 1}^N {b_j \partial _{x_j } - } \partial _t , (t,x) \in \mathbb{R}^{N + 1} . $$

(6.2)