The critical Sobolev inequalities in Besov spaces and regularity criterion to some semi-linear evolution equationsMathematische Zeitschrift - Tập 242 - Trang 251-278 - 2002
Hideo Kozono, Takayoshi Ogawa, Yasushi Taniuchi
We show the critical Sobolev inequalities in the Besov spaces with the logarithmic form such as Brezis-Gallouet-Wainger and Beale-Kato-Majda. As an application of those inequalities, the regularity problem under the critical condition to the Navier-Stokes equations, the Euler equations in
${mathbb R}^n$
and the gradient flow to the harmonic map to the sphere a...... hiện toàn bộ
Computing motivic zeta functions on log smooth modelsMathematische Zeitschrift - Tập 295 - Trang 427-462 - 2019
Emmanuel Bultot, Johannes Nicaise
We give an explicit formula for the motivic zeta function in terms of a log smooth model. It generalizes the classical formulas for snc-models, but it gives rise to much fewer candidate poles, in general. This formula plays an essential role in recent work on motivic zeta functions of degenerating Calabi–Yau varieties by the second-named author and his collaborators. As a further illustration, we ...... hiện toàn bộ
On the volume of graded linear series and Monge–Ampère massMathematische Zeitschrift - Tập 275 - Trang 233-243 - 2012
Tomoyuki Hisamoto
We give an analytic description of the volume of a graded linear series, as the Monge–Ampère mass of a certain equilibrium metric associated to any smooth Hermitian metric on the line bundle. We also show the continuity of this equilibrium metric on some Zariski open subset, under a geometric assumption.