A Liouville theorem for nonlinear elliptic systems with isotropic nonlinearities
A Liouville theorem for solutions of the Monge–Ampère equation with periodic data
A Liouville type theorem for -harmonic functions on minimal submanifolds in
A Liouville-type theorem for elliptic systems
A Liouville-type theorem for the p-laplacian with potential term
A Liouville-type theorem for very weak solutions of nonlinear partial differential equations.
A Littlewood-Paley type inequality with applications to the elliptic Dirichlet problem
Let L be a strictly elliptic second order operator on a bounded domain Ω ⊂ ℝⁿ. Let u be a solution to in Ω, u = 0 on ∂Ω. Sufficient conditions on two measures, μ and ν defined on Ω, are established which imply that the norm of |∇u| is dominated by the norms of and . If we replace |∇u| by a local Hölder norm of u, the conditions on μ and ν can be significantly weaker.
A local approach to some non-linear evolution equations of hyperbolic type
A local -error analysis of the streamline diffusion method for nonstationary convection-diffusion systems
A local projection stabilization finite element method with nonlinear crosswind diffusion for convection-diffusion-reaction equations
An extension of the local projection stabilization (LPS) finite element method for convection-diffusion-reaction equations is presented and analyzed, both in the steady-state and the transient setting. In addition to the standard LPS method, a nonlinear crosswind diffusion term is introduced that accounts for the reduction of spurious oscillations. The existence of a solution can be proved and, depending on the choice of the stabilization parameter, also its uniqueness. Error estimates are derived...
A local version of the generalized retract theorem of Ważewski with applications in the theory of partial differential equations of first order
A localized orthogonal decomposition method for semi-linear elliptic problems
In this paper we propose and analyze a localized orthogonal decomposition (LOD) method for solving semi-linear elliptic problems with heterogeneous and highly variable coefficient functions. This Galerkin-type method is based on a generalized finite element basis that spans a low dimensional multiscale space. The basis is assembled by performing localized linear fine-scale computations on small patches that have a diameter of order H | log (H) | where H is the coarse mesh size. Without any assumptions...
A locally contractive metric for systems of conservation laws
A logarithmic extension of the Hölder inequality.
A logarithmic Gauss curvature flow and the Minkowski problem
A logarithmic regularity criterion for 3D Navier-Stokes system in a bounded domain
This paper proves a logarithmic regularity criterion for 3D Navier-Stokes system in a bounded domain with the Navier-type boundary condition.
A look on some results about Camassa–Holm type equations
We present an overview of some contributions of the author regarding Camassa--Holm type equations. We show that an equation unifying both Camassa--Holm and Novikov equations can be derived using the invariance under certain suitable scaling, conservation of the Sobolev norm and existence of peakon solutions. Qualitative analysis of the two-peakon dynamics is given.
A lower bound for the error term in Weyl’s law for certain Heisenberg manifolds, II
This article is concerned with estimations from below for the remainder term in Weyl’s law for the spectral counting function of certain rational (2ℓ + 1)-dimensional Heisenberg manifolds. Concentrating on the case of odd ℓ, it continues the work done in part I [21] which dealt with even ℓ.
A lower bound for the gradient of -harmonic functions.
A lower bound for the principal eigenvalue of the Stokes operator in a random domain
This article is dedicated to localization of the principal eigenvalue (PE) of the Stokes operator acting on solenoidal vector fields that vanish outside a large random domain modeling the pore space in a cubic block of porous material with disordered micro-structure. Its main result is an asymptotically deterministic lower bound for the PE of the sum of a low compressibility approximation to the Stokes operator and a small scaled random potential term, which is applied to produce a similar bound...