Regularity for almost-minimizers of variable coefficient Bernoulli-type functionalsMathematische Zeitschrift - Tập 299 - Trang 2131-2169 - 2021
Guy David, Max Engelstein, Mariana Smit Vega Garcia, Tatiana Toro
In David et al. (Adv Math 350:1109–1192, 2019) and David and Toro (Regularity of almost minimizers with free boundary. Calculus of variations and PDEs, 2020), the authors studied almost minimizers for functionals of the type first studied by Alt and Caffarelli (J Reine Angew Math 325:105–144, 1981) and Alt et al. (Trans Am Math Soc 282:431–461, 1984). In this paper we study the regularity of almos...... hiện toàn bộ
The Sato–Tate distribution in thin parametric families of elliptic curvesMathematische Zeitschrift - Tập 290 - Trang 831-855 - 2018
Régis de la Bretèche, Min Sha, Igor E. Shparlinski, José Felipe Voloch
We obtain new results concerning the Sato–Tate conjecture on the distribution of Frobenius traces over single and double parametric families of elliptic curves. We consider these curves for values of parameters having prescribed arithmetic structure: product sets, geometric progressions, and most significantly prime numbers. In particular, some families are much thinner than the ones previously st...... hiện toàn bộ
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