A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
The article derives gradient estimations for semilinear equations on geometric flows.
Researchers solve an inverse problem for a semilinear elliptic equation on complex manifolds.
Derives matrix Harnack inequalities for semilinear heat equations on manifolds.
The paper proves Liouville theorems and nonexistence results for semilinear equations on pseudo-Hermitian manifolds.
Paper proves a Liouville theorem for a generalized elliptic equation on H-type groups.
Trivial solution proof for heat equation on certain manifolds.
The paper classifies solutions to semilinear equations on curved spaces.
Derives Li & Yau estimates for heat equations on manifolds.
Sharp conditions found for solving heat equation on Riemannian manifolds.
Paper proves no nontrivial solutions to certain elliptic equations on graphs.
Classifies self-similar solutions for heat equations with positive speed.
The paper classifies solutions to a specific elliptic equation in the Heisenberg group.
Study semilinear equations on weighted manifolds to prove rigidity.
Measuring wave sources uniquely identifies manifold properties.
In this paper, we investigate the problem of blow up and sharp upper bound estimates of the lifespan for the solutions to the semilinear wave equations, posed on asymptotically Euclidean manifolds. Here the metric is assumed to be exponential perturbation of the spherical symmetric, long range asymptotically Euclidean …
Deep neural nets solve complex insurance math equations.
We show that a wide range of overdetermined boundary problems for semilinear equations with position-dependent nonlinearities admits nontrivial solutions. The result holds true both on the Euclidean space and on compact Riemannian manifolds. As a byproduct of the proofs we also obtain some rigidity, or partial symmetry…
We consider a semilinear parabolic degenerated Hamilton-Jacobi-Bellman (HJB) equation with singularity which is related to a stochastic control problem with fuel constraint. The fuel constraint translates into a singular initial condition for the HJB equation. We first propose a transformation based on a change of vari…
New approach simplifies proof of wave equations on black holes.
We introduce a method for solving Calderón type inverse problems for semilinear equations with power type nonlinearities. The method is based on higher order linearizations, and it allows one to solve inverse problems for certain nonlinear equations in cases where the solution for a corresponding linear equation is not…
We consider the Dirichlet problem for semilinear elliptic equations on a bounded domain which is diffeomorphic to a ball and investigate bifurcation from a given (trivial) branch of solutions, where the radius of the ball serves as bifurcation parameter. Our methods are based on well known results from variational bifu…
Study on ground states of semilinear elliptic equations with various potential wells.
Assume that where is a double-well potential. Under certain conditions on the Lipschitz constant of on , we prove that arbitrary bounded global solutions of the semilinear equation on hyperbolic space $\HH^n$ must reduce to functions of one variable provided they admit asympto…
Paper introduces a new method to solve complex PDEs efficiently.
The paper establishes scattering theory for wave equations on Schwarzschild spacetime.
Nonexistence results for semilinear parabolic and hyperbolic inequalities on metric graphs
Study asymptotically almost periodic solutions on real hyperbolic manifolds.
We show that a wide class of geometrically defined overdetermined semilinear partial differential equations may be explicitly prolonged to obtain closed systems. As a consequence, in the case of linear equations we extract sharp bounds on the dimension of the solution space.
The goal of this paper is to clarify when a semilinear stochastic partial differential equation driven by Lévy processes admits an affine realization. Our results are accompanied by several examples arising in natural sciences and economics.
In this paper, we generalize the Gauduchon metrics on a compact complex manifold and define the functions on the space of its hermitian metrics.
We extend the viscosity solution characterization proved in [5] for call/put American option prices to the case of a general payoff function in a multi-dimensional setting: the price satisfies a semilinear re-action/diffusion type equation. Based on this, we propose two new numerical schemes inspired by the branching p…
Paper solves portfolio problem using improved stochastic methods.
New method solves complex curvature equations.
Sharp decay found for solutions of a specific equation in Lie groups.
We answer affirmatively a question of Aviles posed in 1983, concerning the construction of singular solutions of semilinear equations without using phase-plane analysis. Fully exploiting the semilinearity and the stability of the linearized operator in any dimension, our techniques involve a careful gluing in weighted …
We generalise the semi-Riemannian Morse index theorem to elliptic systems of partial differential equations on star-shaped domains. Moreover, we apply our theorem to bifurcation from a branch of trivial solutions of semilinear systems, where the bifurcation parameter is introduced by shrinking the domain to a point. Th…
We demonstrate a family of Strichartz estimates for the conformally invariant Klein-Gordon equation on a class of asymptotically de Sitter spaces with C^2 metrics by using well-known local Strichartz estimates and a rescaling argument. This class of metrics includes de Sitter space. We also give an application of the e…
Consider a nontrivial solution to a semilinear elliptic system of first order with smooth coefficients defined over an -dimensional manifold. Assume the operator has the strong unique continuation property. We show that the zero set of the solution is contained in a countable union of smooth -dimensional subm…
Study solves inverse problems for equations with fractional nonlinearities.
The paper explores symmetry in solutions of semilinear PDEs on Riemannian domains.
Study deep neural nets for solving complex insurance equations.
We construct asymptotically Euclidean solutions of the vacuum Einstein constraint equations with an apparent horizon boundary condition. Specifically, we give sufficient conditions for the constant mean curvature conformal method to generate such solutions. The method of proof is based on the barrier method used by Ise…
In this paper, we construct a Rabinowitz-Floer type homology for a class of non-linear problems having a \emph{starshaped} potential; we consider some equivariant cases as well. We give an explicit computation of the homology and we apply it to obtain results of existence and multiplicity of solutions for several model…
In this article we prove a family of local (in time) weighted Strichartz estimates with derivative losses for the Klein-Gordon equation on asymptotically de Sitter spaces and provide a heuristic argument for the non-existence of a global dispersive estimate on these spaces. The weights in the estimates depend on the ma…
We use probabilistic methods to study classical solutions for systems of interacting semilinear parabolic partial differential equations. In a modeling framework for a financial market with interacting Ito and point processes, such PDEs are shown to provide a natural description for the solution of hedging and valuatio…
New Kelvin transform for anisotropic elliptic problems.
Study on smoothness of solutions to nonlinear equations on Riemannian manifolds.
We study conditions for existence, uniqueness and invariance of the comprehensive nonlinear valuation equations first introduced in Pallavicini et al (2011). These equations take the form of semilinear PDEs and Forward-Backward Stochastic Differential Equations (FBSDEs). After summarizing the cash flows definitions all…