منابع مشابه
A stochastic differential game for the inhomogeneous -Laplace equation
Given a bounded C domain G ⊂ R and functions g ∈ C(∂G,R) and h ∈ C(Ḡ,R \ {0}), let u denote the unique viscosity solution to the equation −2∆∞u = h in G with boundary data g. We provide a representation for u as the value of a two-player zero-sum stochastic differential game. AMS 2000 subject classifications: 91A15, 91A23, 35J70, 49L20
متن کاملLog-laplace Distributions
We present a comprehensive theory and review historical development of the log-Laplace distributions, which can be thought of as exponential functions of skew Laplace laws and have power tail behavior at zero and infinity. We give new results on their properties, representations, and characterizations, discuss estimation of their parameters, and briefly review their applications. AMS Subject Cl...
متن کاملA Laplace Stochastic Frontier Model
We propose a Laplace stochastic frontier model as an alternative to the traditional model with normal errors. An interesting feature of the Laplace model is that the distribution of inefficiency conditional on the composed error is constant for positive values of the composed error, but varies for negative values. Therefore, it may be ideally suited for analyzing industries with many forms on o...
متن کاملThe Laplace Equation
Definition 1. Among the most important and ubiquitous of all partial differential equations is Laplace’s Equation: ∆u = 0, where the Laplacian operator ∆ acts on the function u : U → R (U is open in R) by taking the sum of the unmixed partial derivatives. For example: n = 1: ∆u = ∂ 2u ∂x2 = u = 0 In this simple case, the solution u = ax + b is found by integrating twice. n = 2: ∆u = ∂ 2u ∂x1 + ...
متن کاملInhomogeneous infinity Laplace equation ✩
We present the theory of the viscosity solutions of the inhomogeneous infinity Laplace equation ∂xi u∂xj u∂ 2 xixj u = f in domains in Rn. We show existence and uniqueness of a viscosity solution of the Dirichlet problem under the intrinsic condition f does not change its sign. We also discover a characteristic property, which we call the comparison with standard functions property, of the visc...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: The Annals of Probability
سال: 2004
ISSN: 0091-1798
DOI: 10.1214/009117904000000540