Lie symmetries and criticality of semilinear differential systems.
Lieb–Thirring inequalities on the half-line with critical exponent
We consider the operator in with Dirichlet boundary condition at the origin. For the moments of its negative eigenvalues we prove the bound for any and . This includes a Lieb-Thirring inequality in the critical endpoint case.
Lieb–Thirring inequalities with improved constants
Following Eden and Foias we obtain a matrix version of a generalised Sobolev inequality in one dimension. This allows us to improve on the known estimates of best constants in Lieb–Thirring inequalities for the sum of the negative eigenvalues for multidimensional Schrödinger operators.
Lifshitz tails for some non monotonous random models
In this talk, we describe some recent results on the Lifshitz behavior of the density of states for non monotonous random models. Non monotonous means that the random operator is not a monotonous function of the random variables. The models we consider will mainly be of alloy type but in some cases we also can apply our methods to random displacement models.
Limit behavior of an oscillating thin layer.
Limit behaviour of singular solutions of some semilinear elliptic equations
Limit behaviour of thin insulating layers around multiconnected domains
Limit on the excess negative charge of a dynamic diatomic molecule
Limite semi-classique de l'amplitude de diffusion
Limits of Nonlinear Dirichlet Problems in varying domains.
Linear and nonlinear abstract differential equations of high order
The nonlocal boundary value problems for linear and nonlinear degenerate abstract differential equations of arbitrary order are studied. The equations have the variable coefficients and small parameters in principal part. The separability properties for linear problem, sharp coercive estimates for resolvent, discreetness of spectrum and completeness of root elements of the corresponding differential operator are obtained. Moreover, optimal regularity properties for nonlinear problem is established....
Linear elliptic boundary value problems and weighted Sobolev spaces: a modified approach
Linear elliptic equations with BMO coefficients
We prove an existence and uniqueness theorem for the Dirichlet problem for the equation in an open cube , when belongs to some , with close to 2. Here we assume that the coefficient belongs to the space BMO() of functions of bounded mean oscillation and verifies the condition for a.e. .
Linear elliptic operators with measurable coefficients
Linear Oblique Derivative Problems for the Uniformly Elliptic Hamilton-Jacobi-Bellman Equation.
Linearization and explicit solutions of the minimal surface equations.
We show that the apparatus of support functions, usually used in convex surfaces theory, leads to the linear equation Δh + 2h = 0 describing locally germs of minimal surfaces. Here Δ is the Laplace-Beltrami operator on the standard two-dimensional sphere. It explains the existence of the sum operator of minimal surfaces, introduced recently. In 4-dimensional space the equation Δ h + 2h = 0 becomes inequality wherever the Gauss curvature of a minimal hypersurface is nonzero.
Line-energy Ginzburg-Landau models : zero-energy states
We consider a class of two-dimensional Ginzburg-Landau problems which are characterized by energy density concentrations on a one-dimensional set. In this paper, we investigate the states of vanishing energy. We classify these zero-energy states in the whole space: They are either constant or a vortex. A bounded domain can sustain a zero-energy state only if the domain is a disk and the state a vortex. Our proof is based on specific entropies which lead to a kinetic formulation, and on a careful...
Linking over cones and nontrivial solutions for p-Laplace equations with p-superlinear nonlinearity
Liouville results for -Laplace equations of Lane-Emden-Fowler type
Liouville theorems, a priori estimates, and blow-up rates for solutions of indefinite superlinear parabolic problems
In this paper we establish new nonlinear Liouville theorems for parabolic problems on half spaces. Based on the Liouville theorems, we derive estimates for the blow-up of positive solutions of indefinite parabolic problems and investigate the complete blow-up of these solutions. We also discuss a priori estimates for indefinite elliptic problems.