Diffusion semigroups and diffusion processes corresponding to degenerate divergence form operators. (English) Zbl 0907.47040

The authors study existence and uniqueness problems for semigroups and processes generated by differential operators of the form \[ L_t u=\nabla\cdot a\Delta u+\sigma c\cdot\nabla u. \] Here \(a\) is a symmetric and nonnegative definite matrix, \(\sigma\) the square root of \(a\) and \(c\) is a function. The main aim of the paper is to focus cases where \(a\) and \(c\) have minimal regularity, and \(a\) is allowed to degenerate. Weak and very weak solutions of the parabolic equations \[ \partial_tu+ L_tu= 0 \] are studied.
Reviewer: R.Salvi (Milano)


47D06 One-parameter semigroups and linear evolution equations
47F05 General theory of partial differential operators
35K10 Second-order parabolic equations
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