Related papers: Hypoellipticity and Higher Order Levi Conditions

We investigate a connection between solvability of the Dirichlet problem for an infinitely degenerate elliptic operator and the validity of an Orlicz-Sobolev inequality in the associated subunit metric space. For subelliptic operators it is…

This paper deals with second-order optimality conditions for a quasilinear elliptic control problem with a nonlinear coefficient in the principal part that is countably $PC^2$ (continuous and $C^2$ apart from countably many points). We…

We introduce a class of (possibly) degenerate dispersive equations with a drift. We prove that, under the H\"ormander hypoellipticity condition, the relevant Cauchy problem can be uniquely solved in the Schwartz class, and the solution…

In this paper, we study the regularity assumptions commonly adopted in bilevel optimization with constrained lower-level problems, including the linear independence constraint qualification, the strict complementary slackness condition, and…

We prove optimality conditions for different variational functionals containing left and right Caputo fractional derivatives. A sufficient condition of minimization under an appropriate convexity assumption is given. An Euler-Lagrange…

The purpose of this paper is to investigate the existence of three different weak solutions to a nonlinear elliptic problem that is governed by the weighted {\varphi}-Laplacian operator and subjected to Dirichlet boundary conditions. We…

We show that the exterior derivative operator on a symplectic manifold has a natural decomposition into two linear differential operators, analogous to the Dolbeault operators in complex geometry. These operators map primitive forms into…

We prove that the minimal Euler characteristic of a closed symplectic four-manifold with given fundamental group is often much larger than the minimal Euler characteristic of almost complex closed four-manifolds with the same fundamental…

This paper deals with generalized differentiability and second-order necessary optimality conditions for a box-constrained optimal control problem governed by an exponential semilinear elliptic equation with discrete measures as sources,…

We present condition on higher order asymptotic behaviour of basic sequences in a Banach space ensuring the existence of bounded non-compact strictly singular operator on a subspace. We apply it in asymptotic $\ell_p$ spaces, $1\leq…

We prove a Hardy inequality for uniformly elliptic operators subject to Dirichlet or mixed boundary conditions on domains $\Omega$ with piecewiese smooth boundary in arbitrary Riemannian Manifolds (M, g). Employing an approach of E.B.…

This article is devoted to an investigation of a reality condition of a hyperelliptic loop soliton of higher genus. In the investigation, we have a natural extension of Jacobi am-function for an elliptic curves to that for a hyperelliptic…

We develop classes of one-parameter families (OPF) of operators on $C^\infty_c(\mathbb{C})$ which characterize the behavior of operators associated to the $\bar\partial$-problem in $L^2(\mathbb{C},e^{-2p})$ where $p$ is a subharmonic,…

Ivrii's conjecture asserts that the Cauchy problem is $C^{\infty}$ well-posed for any lower order term if every critical point of the principal symbol is effectively hyperbolic. Effectively hyperbolic critical point is at most triple…

This article establishes a bilinear embedding for second-order divergence-form operators with complex coefficients, characterized by the simultaneous presence of first-order terms and negative potentials. This work provides a further…

In the work, the property of the second-order subdifferential is studied and second-order optimality conditions are obtained for the minimization problem. We also obtained necessary and sufficient conditions for an extremum for the extremal…

The global analytic hypoellipticity is proved for a class of second order partial differential equations with non-negative characteristic form globally defined on the torus. The class considered in this work generalizes at some degree the…

We consider Toeplitz operators associated with the renormalized Bochner-Laplacian on high tensor powers of a positive line bundle on a compact symplectic manifold. We study the asymptotic behavior, in the semiclassical limit, of low-lying…

Realizations of differential operators subject to differential boundary conditions on manifolds with conical singularities are shown to have a bounded $H_{\infty}$-calculus in appropriate $L_{p}$-Sobolev spaces provided suitable conditions…

In this paper, we consider conditions that a higher order derivative preserve in conditional expectation operator for a generic nonlinear random variable. Also, the paper introduces higher order derivatives of the Expected Shortfall for a…