Notes on the result of solutions of the equilibrium equations
In this short note, we correct some expressions obtained by Wang et al. (Bound. Value Probl. 2015:230, 2015). The corrected expressions will be useful for evaluating the boundary behaviors of solutions of modified equilibrium equations with finite mass subject. Moreover, the correction of Theorem 2.1 is also given.
Boundary value behaviors for solutions of the equilibrium equations with angular velocity
This work is concerned with a mixed boundary value problems for the slow equilibrium equations with prescribed angular velocity. As an application, we find sufficient conditions for the existence and uniqueness of blow-up solutions under weaker conditions.
Cohomology and L-values
In a paper published in 1959, Shimura presented an elegant calculation of the critical values of L-functions attached to elliptic modular forms using the first cohomology group. We will show that a similar calculation is possible for Hilbert modular forms over real quadratic fields using the second cohomology group. We present explicit numerical examples calculated by this method.