Zobrazeno 1 - 10
of 157
pro vyhledávání: '"Mandel, Rainer"'
Publikováno v:
Comptes Rendus. Mathématique, Vol 360, Iss G5, Pp 513-538 (2022)
In this paper, we study nonlinear Helmholtz equations with sign-changing diffusion coefficients on bounded domains. The existence of an orthonormal basis of eigenfunctions is established making use of weak $\mathtt{T}$-coercivity theory. All eigenval
Externí odkaz:
https://doaj.org/article/3b29bbf611e84ae6901811cb32fa2781
Autor:
Mandel, Rainer
We prove optimal Fourier restriction estimates for the unit sphere in two-dimensional Euclidean space. Our results yield weighted versions of the 2D Restriction Conjecture involving the weight functions $(1+|x|)^\alpha(1+|y|)^\beta$ and $(1+|x|+|y|)^
Externí odkaz:
http://arxiv.org/abs/2310.13750
We prove that the biharmonic NLS equation $\Delta^2 u +2\Delta u+(1+\varepsilon)u=|u|^{p-2}u$ in $\mathbb R^d$ has at least $k+1$ different solutions if $\varepsilon>0$ is small enough and $2
Externí odkaz:
http://arxiv.org/abs/2306.03720
Autor:
Mandel, Rainer
We prove $L^p$-$L^q$-estimates for the Restriction-Extension operator acting on block-radial functions with the aid of new oscillatory integral estimates and interpolation results in mixed Lorentz spaces. Similar techniques apply to the Limiting Abso
Externí odkaz:
http://arxiv.org/abs/2303.03020
Autor:
Mandel, Rainer
We prove embeddings and identities for real interpolation spaces between mixed Lorentz spaces. This partly relies on Minkowski's (reverse) integral inequality in Lorentz spaces $L^{p,r}(X)$ under optimal assumptions on the exponents $(p,r)\in (0,\inf
Externí odkaz:
http://arxiv.org/abs/2303.00607
We discuss a time-harmonic inverse scattering problem for a nonlinear Helmholtz equation with compactly supported inhomogeneous scattering objects that are described by a nonlinear refractive index in unbounded free space. Assuming the knowledge of a
Externí odkaz:
http://arxiv.org/abs/2202.05533
Autor:
Mandel, Rainer
We prove interpolation inequalities of Gagliardo-Nirenberg type involving Fourier symbols that vanish on hypersurfaces in $\mathbb{R}^d$.
Comment: Minor errors are corrected and certain Gagliardo-Nirenberg inequalities for the wave and Schr\"odi
Comment: Minor errors are corrected and certain Gagliardo-Nirenberg inequalities for the wave and Schr\"odi
Externí odkaz:
http://arxiv.org/abs/2201.13050
Autor:
Mandel, Rainer
In this paper we investigate the existence of ground states and dual ground states for Maxwell's Equations in $\mathbb{R}^3$ in nonlocal nonlinear metamaterials. We prove that several nonlocal models admit ground states in contrast to their local ana
Externí odkaz:
http://arxiv.org/abs/2110.04006
Autor:
Mandel, Rainer
We show that nonlinear Maxwell Equations in $\R^3$ admit a convenient dual variational formulation that permits to prove the existence of nontrivial solutions via standard variational methods.
Externí odkaz:
http://arxiv.org/abs/2109.00826
In this paper we study nonlinear Helmholtz equations with sign-changing diffusion coefficients on bounded domains. The existence of an orthonormal basis of eigenfunctions is established making use of weak T-coercivity theory. All eigenvalues are prov
Externí odkaz:
http://arxiv.org/abs/2107.14516