Minimal thinness is a notion that describes the smallness of a set at a boundary point. In this paper, we provide tests for minimal thinness for a large class of subordinate killed Brownian motions in bounded C domains, C domains with compact complements and domains above graphs of bounded C functions. AMS 2010 Mathematics Subject Classification: Primary 60J50, 31C40; Secondary 31C35, 60J45, 60...

The work treats smoothing and dispersive properties of solutions to the Schrödinger equation with magnetic potential. Under suitable smallness assumption on the potential involving scale invariant norms we prove smoothing Strichartz estimate for the corresponding Cauchy problem. An application that guarantees absence of pure point spectrum of the corresponding perturbed Laplace operator is disc...

We show that asymptotically hyperbolic initial data satisfying smallness conditions in dimensions n ≥ 3, or fast decay conditions in n ≥ 5, or a genericity condition in n ≥ 9, can be deformed, by a deformation which is supported arbitrarily far in the asymptotic region, to ones which are exactly Kottler (“SchwarzschildadS”) in the asymptotic region.

We establish new convergence results, in strong topologies, for solutions of the parabolic-parabolic Keller–Segel system in the plane, to the corresponding solutions of the parabolic-elliptic model, as a physical parameter goes to zero. Our main tools are suitable space-time estimates, implying the global existence of slowly decaying (in general, nonintegrable) solutions for these models, under...

The work treats smoothing and dispersive properties of solutions to the Schrödinger equation with magnetic potential. Under suitable smallness assumption on the potential involving scale invariant norms we prove smoothing Strichartz estimate for the corresponding Cauchy problem. An application that guarantees absence of pure point spectrum of the corresponding perturbed Laplace operator is disc...

We show that the time evolution of the operator H = −∆ + i(A · ∇+∇ ·A) + V in R satisfies global Strichartz and smoothing estimates under suitable smoothness and decay assumptions on A and V but without any smallness assumptions. We require that zero energy is neither an eigenvalue nor a resonance.

The results on well-posedness of two inverse problems with integral overdetermination a bounded interval for class odd-order evolution equations general nonlinearity are established. Either the right-hand side or boundary data chosen as controls. Assumptions smallness input time required.

The aim of this note is to prove that almost minimizers the perimeter are Reifenberg flat, for a very weak notion minimality. main observation smallness excess at some scale implies all smaller scales.

We study the homogenization of stationary compressible Navier–Stokes–Fourier system in a bounded three dimensional domain perforated with large number very tiny holes. Under suitable assumptions imposed on smallness and distribution holes, we show that homogenized limit remains same without