Lp bounds for Riesz transforms and square roots associated to second order elliptic operators.
Lp estimates for degenerate elliptic equations.
In this note we are going to address the question of when a second order differential operator is controlled by a subelliptic second order differential operator.
Lp estimates of boundary integral equations for some nonlinear boundary value problems.
Lp - Lp'-Estimates for Fourier Integral Operators Related to Hyperbolic Equations.
Lp regularity of the Dirichlet problem for elliptic equations with singular drift.
Lp-Abschätzungen und klassische Lösungen für nichtlineare Wellengleichungen. I.
Lp-Abschätzungen und klassische Lösungen für nichtlineare Wellengleichungen II.
Lp-Decacy Rates for Homogeneous Wave-Equations.
Lp-estimates for the wave equation on the Heisenberg group.
Let £ denote the sub-Laplacian on the Heisenberg group Hm. We prove that ei√£ / (1 - £)α/2 extends to a bounded operator on Lp(Hm), for 1 ≤ p ≤ ∞, when α > (d - 1) |1/p - 1/2|.
Lq - Lr estimates for solutions of the nonstationary Stokes equations in an exterior domain and the Navier-Stokes initial value problems in Lq spaces.
L'unicité du problème de Cauchy : entre Holmgren et Hörmander
Lyapunov center theorem for some nonlinear PDE's : a simple proof
Lyapunov control of a quantum particle in a decaying potential
Lyapunov exponents for the one-dimensional parabolic Anderson model with drift.
Lyapunov functions and -estimates for a class of reaction-diffusion systems
We give a sufficient condition for the existence of a Lyapunov function for the system aₜ = ∇(k(a,c)∇a - h(a,c)∇c), x ∈ Ω, t > 0, , x ∈ Ω, t > 0, for , completed with either a = c = 0, or ∂a/∂n = ∂c/∂n = 0, or k(a,c) ∂a/∂n = h(a,c) ∂c/∂n, c = 0 on ∂Ω × t > 0. Furthermore we study the asymptotic behaviour of the solution and give some uniform -estimates.
Lyapunov Functions for Weak Solutions of Reaction-Diffusion Equations with Discontinuous Interaction Functions and its Applications
In this paper we investigate additional regularity properties for global and trajectory attractors of all globally defined weak solutions of semi-linear parabolic differential reaction-diffusion equations with discontinuous nonlinearities, when initial data uτ ∈ L2(Ω). The main contributions in this paper are: (i) sufficient conditions for the existence of a Lyapunov function for all weak solutions of autonomous differential reaction-diffusion equations with discontinuous and multivalued interaction...