On the Best Constant in the Moser-Onofri-Aubin Inequality

On the Best Constant in the Moser-Onofri-Aubin Inequality

Let S2 be the 2-dimensional unit sphere and let Jα denote the nonlinear functional on the Sobolev space H1,2(S2) defined by Jα(u) = α 4 ∫

On a Sharp Moser-aubin-onofri Inequality for Functions on S2 with Symmetry

Here dw denotes the Lebesgue measure on the unit sphere, normalized to make ∫ S2 dw = 1. The famous Moser-Trudinger inequality says that J1 is bounded below by a non-positive constant C1. Later Onofri [6] showed that C1 can be taken to be 0. (Another proof was also given by OsgoodPhillips-Sarnack [7].) On the other hand, if we restrict Jα to the class of G of functions g for which e2g has centr...

The Euclidean Onofri inequality in higher dimensions

Best Constant in Sobolev Inequality

The equality sign holds in (1) i] u has the Jorm: (3) u(x) = [a + btxI,~',-'] 1-~1~ , where Ix[ = (x~ @ ...-~x~) 1⁄2 and a, b are positive constants. Sobolev inequalities, also called Sobolev imbedding theorems, are very popular among writers in part ial differential equations or in the calculus of variations, and have been investigated by a great number of authors. Nevertheless there is a ques...

the effects of changing roughness on the flow structure in the bends

flow in natural river bends is a complex and turbulent phenomenon which affects the scour and sedimentations and causes an irregular bed topography on the bed. for the reason, the flow hydralics and the parameters which affect the flow to be studied and understand. in this study the effect of bed and wall roughness using the software fluent discussed in a sharp 90-degree flume bend with 40.3cm ...