We develop a generalisation of the original theory of regularity structures,[Hai14], which is
able to treat SPDEs on manifolds with values in vector bundles. Assume $ M $ is a …

We analyze properties of semigroups generated by Schrödinger operators Δ− V or
polyharmonic operators−(− Δ) m, on metric graphs both on L p-spaces and spaces of …

We establish convolution inequalities for Besov spaces $ B_ {p, q}^ s $ and Triebel--Lizorkin
spaces $ F_ {p, q}^ s $. As an application, we study the mapping properties of convolution …

In this paper we show the eventual local positivity property for higher-order heat equations
(including noninteger order). As a consequence, we give a positive answer for an open …

Let m∈ N m∈N, P (D):=∑| α|= 2 m (− 1) ma α D α P(D):=∑_|α|=2m(-1)^ma_αD^α be a 2 m
2m‐order homogeneous elliptic operator with real constant coefficients on R n R^n, and VV …

Let P (D) be a nonnegative homogeneous elliptic operator of order 2m with real constant
coefficients on R n and V be a suitable real measurable function. In this paper, we are …

This paper is concerned with the positivity of solutions to the Cauchy problem for linear and
nonlinear parabolic equations with the biharmonic operator as fourth order elliptic principal …

We study higher-order elliptic operators on one-dimensional ramified structures (networks).
We introduce a general variational framework for fourth-order operators that allows us to …

Fluctuation-induced forces occur generically when long-range correlations (eg, in fluids) are
confined by external bodies. In classical systems, such correlations require specific …

Blow-up in second and fourth order semi-linear parabolic partial differential equations
(PDEs) is considered in bounded regions of one, two and three spatial dimensions with …