L–regularity for Parabolic Operators with Unbounded Time–dependent Coefficients

L^p-Regularity for Elliptic Operators with Unbounded Coefficients

Carleman Inequalities and the Heat Operator

1. Introduction. The unique continuation property is best understood for second-order elliptic operators. The classic paper by Carleman [8] established the strong unique continuation theorem for second-order elliptic operators that need not have analytic coefficients. The powerful technique he used, the so-called " Carleman weighted inequality, " has played a central role in later developments....

Nonautonomous Kolmogorov Parabolic Equations with Unbounded Coefficients

We study a class of elliptic operators A with unbounded coefficients defined in I × R for some unbounded interval I ⊂ R. We prove that, for any s ∈ I, the Cauchy problem u(s, ·) = f ∈ Cb(R ) for the parabolic equation Dtu = Au admits a unique bounded classical solution u. This allows to associate an evolution family {G(t, s)} with A, in a natural way. We study the main properties of this evolut...

On maximal parabolic regularity for non-autonomous parabolic operators

We consider linear inhomogeneous non-autonomous parabolic problems associated to sesquilinear forms, with discontinuous dependence of time. We show that for these problems, the property of maximal parabolic regularity can be extrapolated to time integrability exponents r 6= 2. This allows us to prove maximal parabolic L r-regularity for discontinuous non-autonomous second-order divergence form ...

Maximal L Error Analysis of Fems for Nonlinear Parabolic Equations with Nonsmooth Coefficients

The paper is concerned with Lp error analysis of semi-discrete Galerkin FEMs for nonlinear parabolic equations. The classical energy approach relies heavily on the strong regularity assumption of the diffusion coefficient, which may not be satisfied in many physical applications. Here we focus our attention on a general nonlinear parabolic equation (or system) in a convex polygon or polyhedron ...