Related papers: Global boundedness for Generalized Schr\"odinger-T…
The theory of elliptic equations involving singular nonlinearities is well studied topic but the interaction of singular type nonlinearity with nonlocal nonlinearity in elliptic problems has not been investigated so far. In this article, we…
We extend the De Giorgi iteration technique to the vectorial setting. For this we replace the usual scalar truncation operator by a vectorial shortening operator. As an application, we prove local boundedness for local and nonlocal…
In this paper, we investigate the global well-posedness and scattering theory for the defocusing energy supcritical inhomogeneous nonlinear Schr\"odinger equation $iu_t + \Delta u =|x|^{-b} |u|^\alpha u$ in four space dimension, where $s_c…
This paper is devoted to study a fractional Choquard problem with slightly subcritical exponents on bounded domains. When the exponent of the convolution type nonlinearity tends to the fractional critical one in the sense of…
We investigate the decay estimates of global solutions for a class of one-dimensional inhomogeneous nonlinear Schr\"odinger equations. While most existing results focus on spatial dimensions $d\geq2$, the decay properties in one dimension…
We study robust regularity estimates for local minimizers of nonlocal functionals with non-standard growth of $(p,q)$-type and for weak solutions to a related class of nonlocal equations. The main results of this paper are local boundedness…
We establish a weak-strong uniqueness principle for the two-phase Mullins-Sekerka equation in the plane: As long as a classical solution to the evolution problem exists, any weak De Giorgi type varifold solution (see for this notion the…
This paper presents a new column-and-constraint generation method for two-stage robust mixed-integer programs with finite uncertainty sets. Our method combines and extends speed-up techniques used in previous column-and-constraint…
We obtain global well-posedness, scattering, uniform regularity, and global $L^6_{t,x}$ spacetime bounds for energy-space solutions to the defocusing energy-critical nonlinear Schr\"odinger equation in $\R\times\R^4$. Our arguments closely…
Error bound analysis, which estimates the distance of a point to the solution set of an optimization problem using the optimality residual, is a powerful tool for the analysis of first-order optimization algorithms. In this paper, we use…
This paper investigates the existence of normalized solutions for the following Chern-Simons-Schr\"odinger equation: \begin{equation*} \left\{ \begin{array}{ll} -\Delta u+\lambda u+\left(\frac{h^{2}(\vert x\vert)}{\vert…
In this article, we show the global multiplicity result for the following nonlocal singular problem \begin{equation*} (P_\la):\;\quad (-\De)^s u = u^{-q} + \la u^{{2^*_s}-1}, \quad u>0 \; \text{in}\; \Om,\quad u = 0 \; \mbox{in}\; \mb R^n…
We consider the 2D quasi-geostrophic model and its two different regularizations. Global regularity results are established for the regularized models with subcritical or critical indices. The proof of Onsager's conjecture concerning weak…
A boundary value problem on an unbounded domain, associated to difference equations with the Euclidean mean curvature operator is considered. The existence of solutions which are positive on the whole domain and decaying at infinity is…
We consider the Dirichlet problem for a compressible two-fluid model in three dimensions, and obtain the global existence of weak solution with large initial data and independent adiabatic constants \Gamma,\gamma>=9/5. The pressure…
We prove the boundedness of global classical solutions for the semilinear heat equation $u_t-\Delta u= |u|^{p-1}u$ in the whole space $R^n$, with $n\ge 3$ and supercritical power $p>(n+2)/(n-2)$. This is proved {\rmb without any radial…
In this paper, we study the fractional critical Schr\"{o}dinger-Poisson system \[\begin{cases} (-\Delta)^su +\lambda\phi u= \alpha u+\mu|u|^{q-2}u+|u|^{2^*_s-2}u,&~~ \mbox{in}~{\mathbb R}^3,\\ (-\Delta)^t\phi=u^2,&~~ \mbox{in}~{\mathbb…
In this paper, we consider the Schr\"odinger equation with a mass-supercritical focusing nonlinearity, in the exterior of a smooth, compact, convex obstacle of $\R^{d}$ with Dirichlet boundary conditions. We prove that solutions with…
We investigate the existence and the singular limit of normalized ground states for focusing doubly nonlinear Schr\"odinger equations with both standard and concentrated nonlinearities on two-dimensional square grids. First, we provide…
The Schwinger-Keldysh functional renormalization group (fRG) developed in [1] is employed to investigate critical dynamics related to a second-order phase transition. The effective action of model A is expanded to the order of…