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 …

Abstract Let α> 0, H=(− Δ) α+ V (x), V (x) belongs to the higher order Kato class K 2 α (R n).
For 1≤ p≤∞, we prove a polynomial upper bound of‖ e− it H (H+ M)− β‖ L p, L p in terms …

The classic problem of regularity of boundary points for higher-order partial differential
equations (PDEs) is concerned. For second-order elliptic and parabolic equations, this study …

We first highlight the main differences between second order and higher order linear
parabolic equations. Then we survey existing results for the latter, in particular by analyzing …

Blow‐up behavior for the fourth‐order semilinear reaction‐diffusion equation 1 is studied.
For the classic semilinear heat equation from combustion theory 2 various blow‐up patterns …

The classical problem of regularity of boundary characteristic points for semilinear heat
equations with homogeneous Dirichlet conditions is considered. The Petrovskii …

The three-dimensional (3D) Navier–Stokes equations where u=[u, v, w] T is the vector field
and p is the pressure, are considered. Here, Q0⊂ R3×[− 1, 0) is a smooth domain of a …

We obtain heat kernel estimates for a class of fourth order non-uniformly elliptic operators in
two dimensions. Contrary to existing results, the operators considered have symbols that are …

arXiv:1107.3045v2 [math.AP] 12 Oct 2012 Page 1 arXiv:1107.3045v2 [math.AP] 12 Oct 2012
STURMIAN MULTIPLE ZEROS FOR STOKES AND NAVIER–STOKES EQUATIONS IN R3 VIA …

arXiv:1106.4696v1 [math.AP] 23 Jun 2011 Page 1 arXiv:1106.4696v1 [math.AP] 23 Jun
2011 BOUNDARY CHARACTERISTIC POINT REGULARITY FOR SEMILINEAR REACTION-DIFFUSION …