94 research outputs found
Interior Boundaries for Degenerate Elliptic Equations of Second Order Some Theory and Numerical Observations
2010 Mathematics Subject Classification: Primary 35J70; Secondary 35J15, 35D05.For boundary value problems for degenerate-elliptic equations of second order in ⊂ Rn there are cases when a closed surface exists, dividing into two subdomains in such a manner that two new correct boundary value problems can be formulated without introducing new boundary conditions. Such surfaces are called interior boundaries. Some theoretical results regarding the connections between the solutions of the original problem and the two new problems are given. Some numerical experiments using the finite elements method are carried out trying to visualize the effects of the presence of such interior boundary when n = 2. Also some more precise study of the solutions in the case n = 2 is presented
A study on gradient blow up for viscosity solutions of fully nonlinear, uniformly elliptic equations
We investigate sharp conditions for boundary and interior gradient es-
timates of continuous viscosity solutions to fully nonlinear, uniformly ellip-
tic equations under Dirichlet boundary conditions. When these conditions
are violated, there can be blow up of the gradient in the interior or on the
boundary of the domain
New Hardy-Type Inequalities with Singular Weights
2010 Mathematics Subject Classification: 26D10.We prove a new Hardy–type inequality with weights that are possibly singular at internal point and on the boundary of the domain. As an illustration some applications and examples are given
On Principle Eigenvalue for Linear Second Order Elliptic Equations in Divergence Form
2002 Mathematics Subject Classification: 35J15, 35J25, 35B05, 35B50The principle eigenvalue and the maximum principle for second-order elliptic equations is studied. New necessary and sufficient conditions for symmetric and nonsymmetric operators are obtained. Applications for the estimation of the first eigenvalue are given
Theoretical study of nonlinear wave equations with combined power-type nonlinearities with variable coefficients
In this paper, we study the initial boundary value problem for the nonlinear
wave equation with combined power-type nonlinearities with variable
coefficients. The global behavior of the solutions with non-positive and
sub-critical energy is completely investigated. The threshold between the
nonexistence of global in time weak solutions and non-blowing up solutions is
found. For super-critical energy, two new sufficient conditions guaranteeing
nonexistence of global in time solutions are given. One of them is proved for
arbitrary sign of the scalar product of the initial data, while the other one
is derived only for positive sign. Uniqueness and existence of local weak
solutions are proved.Comment: 33 page
The Asymptotic Behaviour of the First Eigenvalue of Linear Second-Order Elliptic Equations in Divergente Form
2000 Mathematics Subject Classification: 35J70, 35P15.The asymptotic of the first eigenvalue for linear second order
elliptic equations in divergence form with large drift is studied. A necessary
and a sufficient condition for the maximum possible rate of the first eigenvalue
is proved
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