Non-linear Neumann's condition for the heat equation : a probabilistic representation using catalytic super-brownian motion
We prove the existence of solutions of the unilateral problem for equations of the type Au - divϕ(u) = μ in Orlicz spaces, where A is a Leray-Lions operator defined on , and .
Some conditions for the existence and uniqueness of solutions of the nonlocal elliptic problem , are given.
The non-local Gel’fand problem, with Dirichlet boundary condition, is studied on an n-dimensional bounded domain Ω. If it is star-shaped, then we have an upper bound of λ for the existence of the solution. We also have infinitely many bendings in λ of the connected component of the solution set in λ,v if Ω is a ball and 3 ≤ n ≤ 9.
We investigate the behavior of weak solutions to the nonlocal Robin problem for linear elliptic divergence second order equations in a neighborhood of a boundary corner point. We find an exponent of the solution's decreasing rate under minimal assumptions on the problem coefficients.
In this paper we study the existence of minimizer for certain constrained variational problems given by functionals with nonlocal terms. This type of functionals are first integrals of evolution equations describing long wave propagation and the existence of minimizer gives the existence and the stability of traveling waves for these equations. Due to loss of compactness, the major problem is to prevent dichotomy of minimizing sequences. Our approach is an alternative to the concentration-compactness...
In this note we give an overview of recent results in the theory of electrorheological fluids and the theory of function spaces with variable exponents. Moreover, we present a detailed and self-contained exposition of shifted -functions that are used in the studies of generalized Newtonian fluids and problems with -structure.