相关论文: On the stabilization problem for nonholonomic dist…

We investigate minimality and stability of periodic brake orbits in natural Lagrangian systems on smooth Riemannian manifolds. We prove that every non-constant periodic brake orbit is not a minimizer of the fixed-time action, for any…

We investigate symmetry properties of solutions to equations of the form $$ -\Delta u = \frac{a}{|x|^2} u + f(|x|, u)$$ in R^N for $N \geq 4$, with at most critical nonlinearities. By using geometric arguments, we prove that solutions with…

In this paper we extend the results of "A strong minimax property of nondegenerate minimal submanifolds" by White, where it is proved that any smooth, compact submanifold, which is a strictly stable critical point for an elliptic parametric…

We derive the solvability and regularity of the Dirichlet problem for fully non-linear elliptic equations possibly with degenerate right-hand side on Hermitian manifolds, through establishing a quantitative version of boundary estimate…

We leverage path differentiability and a recent result on nonsmooth implicit differentiation calculus to give sufficient conditions ensuring that the solution to a monotone inclusion problem will be path differentiable, with formulas for…

We establish a well-posedness and error-estimation framework that solves Hamilton-Jacobi equations by minimizing the least-squares residual of monotone finite-difference discretizations. This approach also applies naturally to second-order…

We consider a class of infinite-dimensional singular stochastic control problems. These can be thought of as spatial monotone follower problems and find applications in spatial models of production and climate transition. Let…

The geometric approach to optimal transport and information theory has triggered the interpretation of probability densities as an infinite-dimensional Riemannian manifold. The most studied Riemannian structures are Otto's metric, yielding…

We prove the exact multiplicity of flat and compact support stable solutions of an autonomous non-Lipschitz semilinear elliptic equation of eigenvalue type according to the dimension N and the two exponents, $0<\alpha<\beta<1$, of the…

The goal of this paper is to prove a comparison principle for viscosity solutions of semilinear Hamilton-Jacobi equations in the space of probability measures. The method involves leveraging differentiability properties of the…

The paper addresses an existence problem for infinite horizon optimal control when the system under control is exponentially stabilizable or stable. Classes of nonlinear control systems for which infinite horizon optimal controls exist are…

We prove that solution operators of elliptic obstacle-type variational inequalities (or, more generally, locally Lipschitz continuous functions possessing certain pointwise-a.e. convexity properties) are Newton differentiable when…

We consider the nonparametric regression problem when the covariates are located on an unknown smooth compact submanifold of a Euclidean space. Under defining a random geometric graph structure over the covariates we analyze the asymptotic…

Nonconvex functionals with spherical symmetry are studied. Existence of one and radial symmetry of all global minimizers is shown with an approach based on convex relaxation.

We give an estimate of the first eigenvalue of the Laplace operator on a complete noncompact stable minimal hypersurface $M$ in a complete simply connected Riemannian manifold with pinched negative sectional curvature. In the same ambient…

Let $(M,g)$ be an asymptotically conical Riemannian manifold having dimension $n\ge 2$, opening angle $\alpha \in (0,\pi/2) \setminus \{\arcsin \frac{1}{2k+1}\}_{k \in \mathbb{N}}$ and positive asymptotic rate. Under the assumption that the…

This paper is concerned with an optimal control problem subject to the $H^1$-critical defocusing semilinear wave equation on a smooth and bounded domain in three spatial dimensions. Due to the criticality of the nonlinearity in the wave…

Let $(M,\bar{g}, e^{-f}d\mu)$ be a complete metric measure space with Bakry-\'Emery Ricci curvature bounded below by a positive constant. We prove that, in $M$, there is no complete two-sided $L_f$-stable immersed $f$-minimal hypersurface…

In this paper, we study real solutions of the nonlinear Helmholtz equation $$ - \Delta u - k^2 u = f(x,u),\qquad x\in \R^N $$ satisfying the asymptotic conditions $$ u(x)=O(|x|^{\frac{1-N}{2}}) \quad \text{and} \quad \frac{\partial^2…

By using variational techniques we provide new existence results for Yamabe-type equations with subcritical perturbations set on a compact $d$-dimensional ($d\geq 3$) Riemannian manifold without boundary. As a direct consequence of our main…