The second edition of this book has a new title that more accurately reflects the table of
contents. Over the past few years, many new results have been proven in the field of partial …

We find necessary and sufficient conditions for the validity of weighted Rellich and Calderón–
Zygmund inequalities with respect to L^ p L p-norm, 1 ≤ p ≤ ∞ 1≤ p≤∞, for functions in …

We obtain the basic results concerning the problem of constructing operator realizations of
the formal differential expression $\nabla\cdot a\cdot\nabla-b\cdot\nabla $ with measurable …

Elliptic operators with unbounded diffusion coefficients in Lp spaces Page 1 Ann. Sc. Norm.
Super. Pisa Cl. Sci. (5) Vol. XI (2012), 303-340 Elliptic operators with unbounded diffusion …

We consider a class of degenerate Ornstein‐Uhlenbeck operators in article amssymb empty
R^N\!, of the kind article amssymb empty A ≡ ∑ _ i, j= 1^ p_ 0 a_ ij (x) ∂ _ x_ i x_ j^ 2+ ∑ …

We show that the realization Ap of the elliptic operator Au= div (Q∇ u)+ F⋅∇ u+ Vu in Lp
(RN, RN), p∈[1,+∞[, generates a strongly continuous semigroup, and we determine its …

We prove that, for α>2, NN-2+c<p<∞, the operator Lu=(1+|x|^α)Δu+c|x|^α-1x|x|⋅∇
generates an analytic semigroup in L^p, which is contractive if and only if p≥N+α-2N-2+c …

We consider the Schrödinger type operator A=(1+| x|^ α) Δ-| x|^ β A=(1+| x| α) Δ-| x| β, for α ∈
0, 2 α∈ 0, 2 and β ≥ 0 β≥ 0. We prove that, for any p ∈ (1, ∞) p∈(1,∞), the minimal …

We show that a realization of the operator L=| x|^ α Δ+ c| x|^ α-1 x| x| ⋅ ∇-b| x|^ α-2 L=| x| α
Δ+ c| x| α-1 x| x|·∇-b| x| α-2 generates a semigroup in L^ p (R^ N) L p (RN) if and only if …

We find necessary and sufficient conditions for the validity of weighted Rellich inequalities in
L^ p L p, 1 ≤ p ≤ ∞ 1≤ p≤∞, for functions in bounded domains vanishing at the …