Stochastic Modeling and Regularity of the Nonlinear Elliptic Curl-Curl Equation

Solvability and Regularity for an Elliptic System Prescribing the Curl, Divergence, and Partial Trace of a Vector Field on Sobolev-class Domains

Non-linear elliptic systems with measure-valued right hand side

We prove existence of a solution u for the nonlinear elliptic system -div a(x,u,Du) =/ i in V(Q,), u = 0 on dfl where \x is Radon measure on Q with finite mass. In particular we show that if the coercivity rate of a lies in the range (1,2 — ^] then u is approximately differentiable and the equation holds with Du replaced by ap Du. The proof relies on an approximation of // by smooth functions f...

Local Well-posedness of the Yang-mills Equation in the Temporal Gauge below the Energy Norm

We show that the Yang-Mills equation in three dimensions in the Temporal gauge is locally well-posed in Hs for s > 3/4 if the Hs norm is sufficiently small. The temporal gauge is slightly less convenient technically than the more popular Coulomb gauge, but has the advantage of uniqueness even for large initial data, and does not require solving a nonlinear elliptic problem. To handle the tempor...

Curl Size and Pelt Color Determination of Zandi Lambs Using Image Processing and Artificial Neural Network

In this study, a method based on using image processing and artificial neural network is introduced to determine pelt color and curl size of newborn lambs in Zandi sheep. The data was collected from 300 newborn lambs reared in the Zandi sheep breeding centre of Khojir, Tehran. Primarily, curl size and pelt color of new born lambs was recorded by experienced appraisers, and at the same time, sev...

AN H s , p ( curl ; Ω ) ESTIMATE FOR THE MAXWELL SYSTEM MANAS KAR AND MOURAD

We derive an H 0 (curl; Ω) estimate for the solutions of the Maxwell type equations modeled with anisotropic and W s,∞(Ω)-regular coefficients. Here, we obtain the regularity of the solutions for the integrability and smoothness indices (p, s) in a plan domain characterized by the apriori lower/upper bounds of a and the apriori upper bound of its Hölder semi-norm of order s. The proof relies on...