Maximum principles and minimal surfaces
Maximum principles and the method of moving planes for a class of degenerate elliptic linear operators
We deal with maximum principles for a class of linear, degenerate elliptic differential operators of the second order. In particular the Weak and Strong Maximum Principles are shown to hold for this class of operators in bounded domains, as well as a Hopf type lemma, under suitable hypothesis on the degeneracy set of the operator. We derive, as consequences of these principles, some generalized maximum principles and an a priori estimate on the solutions of the Dirichlet problem for the linear equation....
Maximum principles for a class of nonlinear second-order elliptic boundary value problems in divergence form.
Maximum Principles for Linear, Non-Unifomly Elliptic Operators with Measurable Coefficients.
Maximum principles for parabolic systems coupled in both first-order and zero-order terms.
Maximum principles for some quasilinear second order partial differential equations
Maximum principles, sliding techniques and applications to nonlocal equations.
Maximum-norm resolvent estimates for elliptic finite element operators on nonquasiuniform triangulations
In recent years several papers have been devoted to stability and smoothing properties in maximum-norm of finite element discretizations of parabolic problems. Using the theory of analytic semigroups it has been possible to rephrase such properties as bounds for the resolvent of the associated discrete elliptic operator. In all these cases the triangulations of the spatial domain has been assumed to be quasiuniform. In the present paper we show a resolvent estimate, in one and two space dimensions,...
Maximum-norm resolvent estimates for elliptic finite element operators on nonquasiuniform triangulations
In recent years several papers have been devoted to stability and smoothing properties in maximum-norm of finite element discretizations of parabolic problems. Using the theory of analytic semigroups it has been possible to rephrase such properties as bounds for the resolvent of the associated discrete elliptic operator. In all these cases the triangulations of the spatial domain has been assumed to be quasiuniform. In the present paper we show a resolvent estimate, in one and two space dimensions, under...
Maximum-Norm Stability and Error Estimates in Galerkin Methods for Parabolic Equations in One Space Variable
Maximun Principle and existence of solutions for elliptic systems involving schrödinger operators
Maxwell's equations with incident wave as a field source
Mean curvature and least energy solutions for the critical Neumann problem with weight
In this paper we consider the Neumann problem involving a critical Sobolev exponent. We investigate a combined effect of the coefficient of the critical Sobolev nonlinearity and the mean curvature on the existence and nonexistence of solutions.
Mean curvature and the heat equation.
Mean curvature properties for -Laplace phase transitions
This paper deals with phase transitions corresponding to an energy which is the sum of a kinetic part of -Laplacian type and a double well potential with suitable growth conditions. We prove that level sets of solutions of possessing a certain decay property satisfy a mean curvature equation in a suitable weak viscosity sense. From this, we show that, if the above level sets approach uniformly a hypersurface, the latter has zero mean curvature.
Mean transit time and mean residence time for linear diffusion-convection-reaction transport system.
Mean value and Harnack inequalities for a certain class of degenerate parabolic equations.
In this paper we study the behavior of degenerate parabolic equations of the formv(x) ut(x,t) = Σni,j=1 Dxi (aij(x,t) Dxi u(x,t)),where the coefficients are measurable functions.
Mean value and Harnack inequalities for degenerate parabolic equations
Mean value densities for temperatures
A positive measurable function K on a domain D in is called a mean value density for temperatures if for all temperatures u on D̅. We construct such a density for some domains. The existence of a bounded density and a density which is bounded away from zero on D is also discussed.
Mean value theorems for linear and semi-linear rotation invariant operators