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On a Class of Elliptic Operators with Unbounded Time- and Space-dependent Coefficients in ℝ N
We prove optimal Schauder estimates for classical solutions of the nonhomogeneous Cauchy problem associated with a class of elliptic operators with...
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On the Unique Continuation Properties for Elliptic Operators with Singular Potentials
Let u be a solution to a second order elliptic equation with singular potentials belonging to Kato–Fefferman–Phong’s class in Lipschitz domains. An...
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Monotonicity of control volume methods
Robustness of numerical methods for multiphase flow problems in porous media is important for development of methods to be used in a wide range of...
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Applications of the Differential Calculus to Nonlinear Elliptic Operators with Discontinuous Coefficients
The paper concerns Dirichlet’s problem for second order quasilinear non-divergence form elliptic equations with discontinuous coefficients. We start...
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Fine regularity for elliptic systems with discontinuous ingredients
We propose results on interior Morrey, BMO and Hölder regularity for the strong solutions to linear elliptic systems of order 2 b with discontinuous...
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Worst scenario method in homogenization. Linear case
The paper deals with homogenization of a linear elliptic boundary problem with a specific class of uncertain coefficients describing composite...
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Numerical Convergence of the MPFA O-Method for General Quadrilateral Grids in Two and Three Dimensions
This paper presents the MPFA O-method for quadrilateral grids, and gives convergence rates for the potential and the normal velocities. The...
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Global Existence for a Parabolic-hyperbolic Free Boundary Problem Modelling Tumor Growth
In this paper we study a free boundary problem modelling tumor growth, proposed by A. Friedman in 2004. This free boundary problem involves a...
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On the dynamics of a degenerate parabolic equation: global bifurcation of stationary states and convergence
We study the dynamics of a degenerate parabolic equation with a variable, generally non-smooth diffusion coefficient, which may vanish at some points...
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Strong Solvability of Boundary Value Contact Problems
Strong solvability in Sobolev spaces is proved for a unilateral contact boundary value problem for a class of nonlinear discontinuous operators. The...
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Singular Integral Operators, Morrey Spaces and Fine Regularity of Solutions to PDE's
Boundedness in Morrey spaces is studied for singular integral operators with kernels of mixed homogeneity and their commutators with multiplication...
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Well-posedness in BV t and convergence of a difference scheme for continuous sedimentation in ideal clarifier-thickener units
We consider a scalar conservation law modeling the settling of particles in an ideal clarifier-thickener unit. The conservation law has a nonconvex...
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Strong Solvability of Boundary Value Problems in Elasticity with Unilateral Constraints
Strong solvability in Sobolev spaces is proved for a unilateral boundary value problem for a class of nonlinear discontinuous operators. The operator...
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Estimates of Integral Kernels for Semigroups Associated with Second-Order Elliptic Operators with Singular Coefficients
In this paper we obtain pointwise two-sided estimates for the integral kernel of the semigroup associated with second-order elliptic differential...
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Obstacles Problems with Measure Data and Linear Operators
We give a definition for Obstacle Problems with measure data and general obstacles. For such problems we prove existence and uniqueness of solutions...
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An elliptic boundary problem for a system involving a discontinuous weight
In a recent paper, Agranovich, Denk and Faierman dealt with a priori estimates, completeness, Abel-Lidskii summability, and eigenvalue asymptotics...