Elliptic problems with growth in nonreflexive Orlicz spaces and with measure or L1L^1 data

We investigate solutions to nonlinear elliptic Dirichlet problems of the type $$\left\{\begin{array}{cl} - {\rm div} A(x,u,\nabla u)= \mu &\qquad \mathrm{ in}\qquad \Omega, u=0 &\qquad \mathrm{ on}\qquad \partial\Omega, \end{array}\right.$$ where $\Omega$ is a bounded Lipschitz domain in $\mathbb{R}^n$ and $A(x,z,\xi)$ is a Carath\'eodory's function. The growth of~the~monotone vector field $A$ with respect to the $(z,\xi)$ variables is expressed through some $N$-functions $B$ and $P$. We do not require any particular type of growth condition of such functions, so we deal with problems in nonreflexive spaces. When the problem involves measure data and weakly monotone operator, we prove existence. For $L^1$-data problems with strongly monotone operator we infer also uniqueness and regularity of~solutions and their gradients in the scale of Orlicz-Marcinkiewicz spaces

An existence result for the Leray-Lions type operators with discontinuous coefficients

In this paper we prove an existence result for Leray-Lions quasilinear elliptic operator with discontinuous coefficients. The idea of the proof is based on compactness results for the sequences of solutions to regularized problems obtained via the Compensated Compactness, Young measures, and Set-Valued Analysis tools

Do More Expensive Wines Taste Better? Evidence from a Large Sample of Blind Tastings

Individuals who are unaware of the price do not derive more enjoyment from more expensive wine. In a sample of more than 6,000 blind tastings, we find that the correlation between price and overall rating is small and negative, suggesting that individuals on average enjoy more expensive wines slightly less. For individuals with wine training, however, we find indications of a positive, or at any rate non-negative, correlation. Our results are robust to the inclusion of individual fixed effects, and are not driven by outliers: when omitting the top and bottom deciles of the price distribution, our qualitative results are strengthened, and the statistical significance is improved even further. Our results indicate that both the prices of wines and wine recommendations by experts may be poor guides for non-expert wine consumers.Wine; price/quality relation; expertise