Generalized Harnack inequality for semilinear elliptic equations

This paper is concerned with semilinear equations in divergence form \diver(A(x)Du) = f(u) where $f :\R \to [0,\infty)$ is nondecreasing. We prove a sharp Harnack type inequality for nonnegative solutions which is closely connected to the classical Keller-Osserman condition for the existence of entire solutions

Theoretical Aspects to the Finnish Credit Cycle

The paper discusses the possibility that the workings of the financial system contributed the boom-bust cycle in the Finnish credit market since the mid-1980s. We begin with a review of the most prominent theoretical arguments about the role of "financial factors". Also the main findings of a vast empirical literature are summed up. This is followed by a description of the salient features of the Finnish credit cycle and the associated banking crisis. The evolution of credit stocks and interest rates are then analyzed on a relatively high level of aggregation from the perspective of the theoretical arguments discussed. The main conclusions are: First, changes in the balance sheets of firms and households very likely contributed to both the rapid growth of credit in the late 1980s and its subsequent steep contraction. Second, the observations are also consistent with the conjecture that supply of bank credit very likely increased in the late 1980s and contracted in the early 1990 relative to other sources of credit. Third, some differences observed in the behaviour of different bank groups suggest that moral hazard related to underpriced bank liabilities may have contributed to the growth of lending in the boom period, and problems with capital adequacy may have constrained bank lending in the early 1990s. Stylized facts are consistent with these conjectures. However, to reliably infer about these moral hazard and credit crunch hypotheses, in-depth analysis of bank behaviour with micro data is required. Similarly, ascertaining the role of borrower balance sheets requires analysis of borrowers of different characteristics.credit cycle; financial factors; lending policies; moral hazard; credit crunch

Credit Crunch or Collateral Squeeze? An Empirical Analysis of Credit Supply of the Finnish Local Banks in 1990–1992

The paper examines the determination of bank lending in the early 1990s with the data on 393 savings and cooperative banks. Particular attention is paid to the respective roles of bank capital and costs on the one hand and borrower quality on the other hand. The findings do not support the hypothesis of a general credit crunch caused by capital insufficiency. Some findings suggest, nevertheless, that regulatory pressures and perhaps distractions caused by restructuring may have had a negative effect on lending by the savings banks and some cooperative banks. In addition there is some evidence that weak capital contributed positively to credit growth of some subset of banks in 1992. This moral hazard behaviour differs, however, from that observed in a companion paper for the late 1980s. This time the banks resorting to a "gamble for resurrection" were not the weakest banks in terms of capitalization or credit riksks, but more in the middle of the spectrum: not so strong that they could take the full losses associated with non-performing assets and not so weak that regulatory pressures had strongly constrained additional lending to ailing customers. These banks were typically cooperative banks rather than savings banks as in the 1980s. On the other hand, weak borrower quality — measured mainly by the share of nonperforming assets — contributed significantly to the low growth and contraction of bank lending in 1991 and 1992. In sum, bank capital was not a major factor in the contraction of lending in the early 1990s but lending was significantly reduced by weak borrower quality.credit crunch; capital crunch; borrower quality; collateral squeeze; bank lending

Minimality via second variation for microphase separation of diblock copolymer melts

We consider a non local isoperimetric problem arising as the sharp interface limit of the Ohta-Kawasaki free energy introduced to model microphase separation of diblock copolymers. We perform a second order variational analysis that allows us to provide a quantitative second order minimality condition. We show that critical configurations with positive second variation are indeed strict local minimizers of the nonlocal perimeter. Moreover we provide, via a suitable quantitative inequality of isoperimetric type, an estimate of the deviation from minimality for configurations close to the minimum in the $L^1$ topology