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Yawei Wei

Publications and source records attributed to Yawei Wei.

23 records · Page 2Linked to original sources
arXiv2024

Properties of fractional p-Laplace equations with sign-changing potential

In this paper, we consider the nonlinear equation involving the fractional p-Laplacian with sign-changing potential. This model draws inspiration from De Giorgi Conjecture. There are two main results in this paper. Firstly, we obtain that the solution is radially symmetric within the bounded domain, by applying the moving plane method. Secondly, by exploiting the idea of the sliding method, we construct the appropriate auxiliary functions to prove that the solution is monotone increasing in some direction in the unbounded domain. The different properties of the solution in bounded and unbounded domains are mainly attributed to the inherent non-locality of the fractional p-Laplacian.

math.AP↗
arXiv2023

Mean Field Games with infinitely degenerate diffusion and non-coercive Hamiltonian

In this paper, we consider a class of infinitely degenerate partial differential systems to obtain the Nash equilibria in the mean field games. The degeneracy in the diffusion and the Hamiltonian may be different. This feature brings difficulties to the uniform boundness of the solutions, which is central to the existence and regularity results. First, from the perspective of the value function in the stochastic optimal control problems, we prove the Lipschitz continuity and the semiconcavity for the solutions of the Hamilton-Jacobi equations (HJE). Then the existence of the weak solutions for the degenerate systems is obtained via a vanishing viscosity method. Furthermore, by constructing an auxiliary function, we conclude the regularity of the viscosity solution for the HJE in the almost everywhere sense.

math.AP↗
arXiv2023

Degenerate Mean Field Games with Hörmander diffusion

In this paper, we study a class of degenerate mean field game systems arising from the mean field games with Hörmander diffusion, where the generic player may have a ``forbidden'' direction at some point. Here we prove the existence and uniqueness of the classical solutions in weighted Hölder spaces for the PDE systems, which describe the Nash equilibria in the games. The degeneracy causes the lack of commutation of vector fields and the fundamental solution which are the main difficulties in the proof of the global Schauder estimate and the weak maximum principle. Based on the idea of the localizing technique and the local homogeneity of degenerate operators, we extend the maximum regularity result and obtain the global Schauder estimates. For the weak maximum principle, we construct a subsolution instead of the fundamental solution of the degenerate operators.

math.AP↗
arXiv2012

The Mellin-Edge Quantisation for Corner Operators

We establish a quantisation of corner-degenerate symbols, here called Mellin-edge quantisation, on a manifold $M$ with second order singularities. The typical ingredients come from the "most singular" stratum of $M$ which is a second order edge where the infinite transversal cone has a base $B$ that is itself a manifold with smooth edge. The resulting operator-valued amplitude functions on the second order edge are formulated purely in terms of Mellin symbols taking values in the edge algebra over $B.$ In this respect our result is formally analogous to a quantisation rule of a joint paper with J. Gil and J. Seiler for the simpler case of edge-degenerate symbols that corresponds to the singularity order 1. However, from the singularity order 2 on there appear new substantial difficulties for the first time, partly caused by the edge singularities of the cone over $B$ that tend to infinity.

math.AP↗