Sentence examples for class of radial from inspiring English sources

We consider a special class of radial solutions of semilinear equations −Δu= g u) in the unit ball of Rn.

Recently it was shown in [18], [19], [15] that there exists a large class of radial initial data such that the corresponding solutions blow up in finite time.

A class of radial measuresμon Rnis defined so that integrable harmonic functionsfon Rnmay be characterized as solutions of convolution equationsf*μ=f.

The purpose of this paper is to investigate Lp boundedness properties of a certain class of radial Fourier integral operators on the space X.

This oscillator, a modified Poincaré oscillator [21], belongs to the class of radial isochron limit cycles (RILC) due to its radial symmetry (see Materials and Methods).

These results are generalized to a large class of (L_{p}) radial valuations.

In the following, we introduce a new class of lower radial tangent cones and two new kinds of second-order tangent sets.

In this paper, we introduce a new class of lower radial tangent cones and two new kinds of second-order tangent sets, using which we introduce four new kinds of second-order tangent derivatives.

Let D be an arbitrary domain in R n and A a denote the class of nonnegative radial potentials a ( P ), i.e. 0 ≤ a ( P ) = a ( r ), P = ( r, Θ ) ∈ D, such that a ∈ L loc b ( D ) with some b > n / 2 if n ≥ 4 and with b = 2 if n = 2 or n = 3.

Let C n be an arbitrary domain in R n and A a denote the class of nonnegative radial potentials a ( P ), i.e. 0 ≤ a ( P ) = a ( r ), P = ( r, Θ ) ∈ C n , such that a ∈ L loc b ( C n with some b > n / 2 if n ≥ 4 and with b = 2 if n = 2 or n = 3.

Let D be an arbitrary domain in ({mathbf{R}}^{n}) and (mathscr{A}_{a}) denote the class of nonnegative radial potentials (a(P)), i.e. (0leq a(P =a(r)), (P= r,Theta)in D), such that (ain L_{mathrm{loc}}^{b}(D)) with some (b> {n}/{2}) if (ngeq4) and with (b=2) if (n=2) or (n=3).