Search results for "BOUNDARY-VALUE PROBLEM"
showing 5 items of 5 documents
Regularity of renormalized solutions to nonlinear elliptic equations away from the support of measure data
2018
We prove boundedness and continuity for solutions to the Dirichlet problem for the equation $$ - {\rm{div}}(a(x,\nabla u)) = h(x,u) + \mu ,\;\;\;\;\;{\rm{in}}\;{\rm{\Omega }} \subset \mathbb{R}^{N},$$ where the left-hand side is a Leray-Lions operator from $$- {W}^{1,p}_0(\Omega)$$ into W−1,p′(Ω) with 1 < p < N, h(x,s) is a Caratheodory function which grows like ∣s∣p−1 and μ is a finite Radon measure. We prove that renormalized solutions, though not globally bounded, are Holder-continuous far from the support of μ.
Partial data inverse problems for Maxwell equations via Carleman estimates
2015
In this article we consider an inverse boundary value problem for the time-harmonic Maxwell equations. We show that the electromagnetic material parameters are determined by boundary measurements where part of the boundary data is measured on a possibly very small set. This is an extension of earlier scalar results of Bukhgeim-Uhlmann and Kenig-Sj\"ostrand-Uhlmann to the Maxwell system. The main contribution is to show that the Carleman estimate approach to scalar partial data inverse problems introduced in those works can be carried over to the Maxwell system.
On Mathematical Modelling of Metals Distribution in Peat Layers
2014
In this paper we consider averaging and finite difference methods for solving the 3-D boundary-value problem in multilayered domain. We consider the metals Fe and Ca concentration in the layered peat blocks. Using experimental data the mathematical model for calculation of concentration of metals in different points in peat layers is developed. A specific feature of these problems is that it is necessary to solve the 3-D boundary-value problems for elliptic type partial differential equations (PDEs) of second order with piece-wise diffusion coefficients in the layered domain. We develop here a finite-difference method for solving of a problem of one, two and three peat blocks with periodica…
THE MATHEMATICAL MODELING OF METALS CONTENT IN PEAT
2015
Metals deposition in peat can aid to evaluate impact of atmospheric or wastewaters pollution and thus can be a good indicator of recent and historical changes in the pollution loading. For peat using in agriculture, industrial, heat production etc. knowledge of peat metals content is important. Experimental determination of metals in peat is very long and expensive work. Using experimental data the mathematical model for calculation of concentrations of metals in different points for different layers is developed. The values of the metals (Ca, Mg, Fe, Sr, Cu, Zn, Mn, Pb, Cr, Ni, Se, Co, Cd, V, Mo) concentrations in different layers in peat taken from Knavu peat bog from four sites are deter…
Multiplicity of Solutions to Elliptic Problems Involving the 1-Laplacian with a Critical Gradient Term
2017
Abstract In the present paper we study the Dirichlet problem for an equation involving the 1-Laplacian and a total variation term as reaction.We prove a strong multiplicity result. Namely, we show that for any positive Radon measure concentrated in a set away from the boundary and singular with respect to a certain capacity, there exists an unbounded solution, and measures supported on disjoint sets generate different solutions.These results can be viewed as the analogue for the 1-Laplacian operator of some known multiplicity results which were first obtained by Ireneo Peral, to whom this article is dedicated, and his collaborators.