Related papers: Extremals for $\alpha$-Strichartz inequalities
In this paper we study the Sobolev Trace Theorem for variable exponent spaces with critical exponents. We find conditions on the best constant in order to guaranty the existence of extremals. Then we give local conditions on the exponents…
We derive a lower bound on the location of global extrema of eigenfunctions for a large class of non-local Schr\"odinger operators in convex domains under Dirichlet exterior conditions, featuring the symbol of the kinetic term, the strength…
In this paper, we establish the linear profile decomposition for the Airy equation with complex or real initial data in $L^2$, respectively. As an application, we obtain a dichotomy result on the existence of maximizers for the symmetric…
In this paper we introduce new characterizations of spectral fractional Laplacian to incorporate nonhomogeneous Dirichlet and Neumann boundary conditions. The classical cases with homogeneous boundary conditions arise as a special case. We…
We investigate the existence, uniqueness, and $L^1$-contractivity of weak solutions to a porous medium equation with fractional diffusion on an evolving hypersurface. To settle the existence, we reformulate the equation as a local problem…
We consider the Lane-Emden equation with a supercritical nonlinearity with an inhomogeneous Dirichlet boundary condition on an infinite cone. Under suitable conditions for the boundary data and the exponent of nonlinearity, we give a…
We give an exact formula for the Bellman function of the weak type of martingale transform. We also give the extremal functions (actually extremal sequences of functions). We find them using the precise form of the Bellman function. The…
By using a suitable topological argument based on cohomological linking and by exploiting a Trudinger-Moser inequality in fractional spaces recently obtained, we prove existence of multiple solutions for a problem involving the nonlinear…
We show that eigenvalues of the Robin Laplacian with a positive boundary parameter $\alpha$ on rectangles and unions of rectangtes satisfy P\'{o}lya-type inequalities, albeit with an exponent smaller than that of the corresponding Weyl…
We study the existence of maximizers for a one-parameter family of Strichartz inequalities on the torus. In general maximizing sequences can fail to be precompact in $L^2(\mathbb T)$, and maximizers can fail to exist. We provide a…
Approximate necessary optimality conditions in terms of Fr\'echet subgradients and normals for a rather general optimization problem with a potentially non-Lipschitzian objective function are established with the aid of Ekeland's…
We consider the adjoint restriction inequality associated to the hypersurface $\{(\tau, \xi) : \tau = \pm|\xi|^2, \;\xi \in \mathbb{R}^d\}$ at the Stein-Tomas exponent. Extremizers exist in all dimensions and extremizing sequences are…
In this paper we give the first result about the precise symmetry and symmetry breaking regions of extremal functions for weighted second-order inequalities. Firstly, based on the work of C.-S. Lin [Comm. Partial Differential Equations,…
We give necessary and sufficient conditions for existence and infinite divisibility of $\alpha$-determinantal processes. For that purpose we use results on negative binomial and ordinary binomial multivariate distributions.
In this paper, the author derives an $O(h^4)$-superconvergence for the piecewise linear Ritz-Galerkin finite element approximations for the second order elliptic equation $-\nabla \cdot(A\nabla u)= f$ equipped with Dirichlet boundary…
Let $X=\mathbb{D}/\Gamma$ be an arbitrary Riemann surface. We establish a necessary and sufficient criterion for $[f]\in T(X)$ to have a Teichm\"uller-type extremal map.
We introduce a containment relation of hypergraphs which respects linear orderings of vertices and investigate associated extremal functions. We extend, by means of a more generally applicable theorem, the n.log n upper bound on the ordered…
In this paper, we investigate the extremal functions for anisotropic Trudinger-Moser inequalities. Our method uses convex symmetrization, the continuity of the supremum function, together with the relation between the supremums of the…
The paper provides new upper and lower bounds for the multivariate Laplace approximation under weak local assumptions. Their range of validity is also given. An application to an integral arising in the extension of the Dixon's identity is…
Eigenvalue interlacing is a useful tool in linear algebra and spectral analysis. In its simplest form, the interlacing inequality states that a rank-one positive perturbation shifts each eigenvalue up, but not further than the next…