On the Critical Semilinear Wave Equation Outside Convex Obstacles
From MaRDI portal
Publication:4874225
DOI10.2307/2152832zbMath0860.35081OpenAlexW4237260572MaRDI QIDQ4874225
Hart F. Smith, Christopher D. Sogge
Publication date: 21 April 1997
Full work available at URL: https://doi.org/10.2307/2152832
Related Items (41)
Scattering for critical radial Neumann waves outside a ball ⋮ Comparable upper and lower bounds for boundary values of Neumann eigenfunctions and tight inclusion of eigenvalues ⋮ On the \(L^p\) norm of spectral clusters for compact manifolds with boundary ⋮ On nonlinear Schrödinger equations in exterior domains ⋮ Global Strichartz estimates for solutions to the wave equation exterior to a convex obstacle ⋮ \(L^p\) eigenfunction bounds for the Hermite operator ⋮ About the wave equation outside two strictly convex obstacles ⋮ Asymptotics of wave models for non star-shaped geometries ⋮ Optimal control of an energy-critical semilinear wave equation in 3D with spatially integrated control constraints ⋮ Dispersion for the wave equation inside strictly convex domains. II: The general case ⋮ Stabilization of the critical semilinear wave equation on non-compact Riemannian manifold ⋮ Lower bounds for nodal sets of Dirichlet and Neumann eigenfunctions ⋮ Survey on the Decay of the Local Energy for the Solutions of the Nonlinear Wave Equation ⋮ Dispersion for the wave equation outside a cylinder in \(\mathbb{R}^3\) ⋮ From spectral cluster to uniform resolvent estimates on compact manifolds ⋮ Scattering for the critical and localised semilinear wave equation ⋮ Strichartz type estimates and the well-posedness of an energy critical 2D wave equation in a bounded domain ⋮ Estimates for a class of oscillatory integrals and decay rates for wave-type equations ⋮ Exponential decay of the local energy for the solutions of critical wave equations outside a convex obstacle ⋮ Lifespan estimates for 2-dimensional semilinear wave equations in asymptotically Euclidean exterior domains ⋮ Strichartz estimates for the wave equation on a 2D model convex domain ⋮ On abstract Strichartz estimates and the Strauss conjecture for nontrapping obstacles ⋮ Dispersion for the wave equation inside strictly convex domains. I: The Friedlander model case ⋮ Global existence for energy critical waves in 3-d domains ⋮ Counterexamples to Strichartz estimates for the wave equation in domains ⋮ Global existence of solutions of the critical semilinear wave equations with variable coefficients outside obstacles ⋮ Null form estimates for ( 1/2,1/2 ) symbols and local existence for a quasilinear Dirichlet-wave equation ⋮ On the energy critical Schrödinger equation in 3D non-trapping domains ⋮ On the growth of the Sobolev norms for the nonlinear Klein-Gordon equation ⋮ New counterexamples to Strichartz estimates for the wave equation on a 2D model convex domain ⋮ Unnamed Item ⋮ Strichartz estimates for the wave equation on manifolds with boundary ⋮ Stabilization and control for the subcritical semilinear wave equation ⋮ Gradient estimates for the eigenfunctions on compact manifolds with boundary and Hörmander Multiplier Theorem ⋮ A parametrix construction for wave equations with \(C^{1,1}\) coefficients ⋮ Eigenfunction estimates for Neumann Laplacian and applications to multiplier problems ⋮ Kakeya-Nikodym averages and \(L^p\)-norms of eigenfunctions ⋮ Approximating pointwise products of Laplacian eigenfunctions ⋮ Scattering for critical wave equations with variable coefficients ⋮ Global existence for a quasilinear wave equation outside of star-shaped domains ⋮ Scattering to a stationary solution for the superquintic radial wave equation outside an obstacle
Cites Work
- Nonlinear small data scattering for the wave and Klein-Gordon equation
- High frequency scattering by a convex obstacle
- Near peak scattering and the corrected Kirchhoff approximation for a convex obstacle
- Concerning the \(L^ p\) norm of spectral clusters for second-order elliptic operators on compact manifolds
- Transformation of boundary problems
- Regularity and asymptotic behaviour of the wave equation with a critical nonlinearity
- Equivalence of glancing hyper-surfaces
- Microlocal parametrices for diffractive boundary value problems
- Restrictions of Fourier transforms to quadratic surfaces and decay of solutions of wave equations
- Regularity results for nonlinear wave equations
- \(L^ p\) regularity for the wave equation with strictly convex obstacles
- On existence and scattering with minimal regularity for semilinear wave equations
- On Strichartz and eigenfunction estimates for low regularity metrics
- A priori estimates for the wave equation and some applications
- Fourier integral operators. I
- The radiation pattern of a diffracted wavenear the shadow boundary
- Egoroy's theorem on a manifold with diffractive boundary
- Semi-linear wave equations
- Regularity for the wave equation with a critical nonlinearity
- Local Smoothing of Fourier Integral Operators and Carleson-Sjolin Estimates
- Grazing rays and reflection of singularities of solutions to wave equations
- The wave front set of the solution of a simple initial-boundary value problem with glancing rays
- Space‐time estimates for null forms and the local existence theorem
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
This page was built for publication: On the Critical Semilinear Wave Equation Outside Convex Obstacles
