Sharp kernel estimates for elliptic operators with second-order discontinuous coefficients

Maximal regularity for elliptic operators with second-order discontinuous coefficients

“…Next we show that, under the assumptions of Theorems 2.1 and 2.2, the generated semigroup e zL consists of integral operators, see [3,11].…”

“…In this section, we recall, without proofs, the main results concerning generation and domain characterization proved in [13,15]. Kernel estimates are, instead, proved in [3,11,16].…”

“…Operators of this form have been widely investigated in previous works. In particular generation properties of analytic semigroups in L p spaces endowed with the Lebesgue measure, sharp kernel estimates and Rellich-type inequalities have been proved (see [3,[10][11][12][13][14][15][16]). Here, we prove that the following parabolic problem associated with L ∂ t u(t) − Lu(t) = f (t), t > 0, u(0) = 0 (2) has maximal L q regularity, that is for each f ∈ L q (0, ∞; X ) there exists u ∈ W 1,q (0, ∞; X ) ∩ L q (0, ∞; D(L)) satisfying (2).…”

Integral representation of solutions using Green function for fractional Hardy equations

“…Towards this, first we establish two sided estimate for the Green function of fractional Hardy operator P . In context to the local case, recently in [18], the authors obtain sharp two sided Green function estimate for second-order elliptic operator of Fuchsian-type on R N .…”

Heat kernel of fractional Laplacian with Hardy drift via desingularizing weights

“…Appendix D). The corresponding result, however, is known, see [18,19], where the authors obtain sharp upper and lower bounds on the heat kernel of the operator ´∇ ¨p1 `c|x| ´2x t xq ¨∇ `δ1…”