Gaussian estimates with best constants for higher-order Schr\"odinger operators with Kato potentials

We establish Gaussian estimates on the heat kernel of a higher-order uniformly elliptic Schr\"odinger operator with variable highest order coefficients and with a Kato class potential. The estimates involve the sharp constant in the Gaussian exponent.Comment: 9 pages; a mistaken example has been removed; to appear in Proc. Amer. Math. So

Higher order linear parabolic equations

We first highlight the main differences between second order and higher order linear parabolic equations. Then we survey existing results for the latter, in particular by analyzing the behavior of the convolution kernels. We illustrate the updated state of art and we suggest several open problems.Comment: Dedicated to Patrizia Pucci. To appear in the the Contemporary Mathematics series of the AM

Monotonicity, continuity and differentiability results for the LpL^p Hardy constant

We consider the $L^p$ Hardy inequality involving the distance to the boundary for a domain in the $n$-dimensional Euclidean space. We study the dependence on $p$ of the corresponding best constant and we prove monotonicity, continuity and differentiability results. The focus is on non-convex domains in which case such constant is in general not explicitly known.Comment: 12 pages; to appear in the Israel Journal of Mathematic

Shape sensitivity analysis of the Hardy constant

We consider the Hardy constant associated with a domain in the $n$-dimensional Euclidean space and we study its variation upon perturbation of the domain. We prove a Fr\'{e}chet differentiability result and establish a Hadamard-type formula for the corresponding derivatives. We also prove a stability result for the minimizers of the Hardy quotient. Finally, we prove stability estimates in terms of the Lebesgue measure of the symmetric difference of domains.Comment: 23 pages; showkeys command remove

The Hardy constant: a review

We present a review of results that have been obtained in the past twenty-five years concerning the $L^p$-Hardy inequality with distance to the boundary. We concentrate on results where the best Hardy constant is either computed exactly or estimated from below.Comment: 7 pages. To appear in the volume "Modern Problems in PDEs and Applications - Extended Abstracts of the 2023 Ghent Analysis and PDE Center Summer School", Research Perspectives Ghent Analysis and PDE Center, Trends in Mathematics, Springer. Editors: M. Chatzakou, J. Restrepo, M. Ruzhansky, B. Torebek, K. Van Bocksta

Determinants of bilateral current account balance between the Eurozone and the United States

[Abstract] Long- and short-run current account balance (CAB) determinants of the nineteen Eurozone (EZ) member states vis-a-vis the United States (US) are examined. Particularly, the competitiveness of the EZ vs the US, the relationship between the current account deficit and the budget deficit (twin deficit), and other factors determining the current account balance are studied. Quarterly data was used in a sample of the nineteen EZ member states with the US as a trading partner over the period 2008 - 2018. It is found that the CAB in the long run has a positive relationship with the real interest rate, real exchange rate, Gross Domestic Product (GDP) per capita, and exchange rate volatility, but a negative relationship with the fiscal balance. In the short run, it is notable that only the real exchange rate affects the current account balance. Finally, policy implications are discussed regarding the determinants of the current account

The gospels-text of Athanasius.

Thesis (Ph.D.)--Boston UniversityThe subject of this Dissertation belongs to the general field of the Patristic studies; specifically, it is connected with the contribution of the Patristic quotations to the Textual Criticism of the New Testament. The main purpose of this study focuses on the investigation of the text of the four Gospels as used by Athanasius. Textual critics of the New Testament, in the past one hundred years, have merely said that Athanasius used the so-called "Neutral Text", but the evidence for such a statement has not yet been given. It is therefore important for us to discover whether this Father actually used the "Neutral Text" or any other type of text. [TRUNCATED