New Sobolev type embeddings for some weighted Banach spaces are established. Using such embeddings and the singular positive radial entire solutions, we construct singular positive weak solutions with a prescribed sin...New Sobolev type embeddings for some weighted Banach spaces are established. Using such embeddings and the singular positive radial entire solutions, we construct singular positive weak solutions with a prescribed singular set for a weighted elliptic equation. Our main results in this paper also provide positive weak solutions with a prescribed singular set to an equation with Hardy potential.展开更多
New embeddings of some weighted Sobolev spaces with weights a(x)and b(x)are established.The weights a(x)and b(x)can be singular.Some applications of these embeddings to a class of degenerate elliptic problems of the f...New embeddings of some weighted Sobolev spaces with weights a(x)and b(x)are established.The weights a(x)and b(x)can be singular.Some applications of these embeddings to a class of degenerate elliptic problems of the form-div(a(x)?u)=b(x)f(x,u)in?,u=0 on??,where?is a bounded or unbounded domain in RN,N 2,are presented.The main results of this paper also give some generalizations of the well-known Caffarelli-Kohn-Nirenberg inequality.展开更多
In this paper,the authors study the gradient estimates for positive weak solutions to the following p-Laplacian equation△_(p)u+au^(σ)=0 on complete noncompact Riemannian manifold,where a,σare two nonzero real const...In this paper,the authors study the gradient estimates for positive weak solutions to the following p-Laplacian equation△_(p)u+au^(σ)=0 on complete noncompact Riemannian manifold,where a,σare two nonzero real constants with p≠2.Using the gradient estimate,they can get the corresponding Lionville theorem.On the other hand,by virtue of the Poincare inequality,they also obtain a Liouville theorem under some integral conditions with respect to positive weak solutions.展开更多
The goal of this paper is to study the mathematical properties of a new model of soil carbon dynamics which is a reaction-diffusion system with a chemotactic term, with the aim to account for the formation of soil agg...The goal of this paper is to study the mathematical properties of a new model of soil carbon dynamics which is a reaction-diffusion system with a chemotactic term, with the aim to account for the formation of soil aggregations in the bacterial and microorganism spatial organization(hot spot in soil). This is a spatial and chemotactic version of MOMOS(Modelling Organic changes by Micro-Organisms of Soil), a model recently introduced by M. Pansu and his group. The authors present here two forms of chemotactic terms, first a"classical" one and second a function which prevents the overcrowding of microorganisms.They prove in each case the existence of a nonnegative global solution, and investigate its uniqueness and the existence of a global attractor for all the solutions.展开更多
基金supported by National Natural Science Foundation of China (Grant Nos. 11171092 and 11571093)
文摘New Sobolev type embeddings for some weighted Banach spaces are established. Using such embeddings and the singular positive radial entire solutions, we construct singular positive weak solutions with a prescribed singular set for a weighted elliptic equation. Our main results in this paper also provide positive weak solutions with a prescribed singular set to an equation with Hardy potential.
基金supported by National Natural Science Foundation of China (Grant Nos. 11171092, 11571093 and 11371117)
文摘New embeddings of some weighted Sobolev spaces with weights a(x)and b(x)are established.The weights a(x)and b(x)can be singular.Some applications of these embeddings to a class of degenerate elliptic problems of the form-div(a(x)?u)=b(x)f(x,u)in?,u=0 on??,where?is a bounded or unbounded domain in RN,N 2,are presented.The main results of this paper also give some generalizations of the well-known Caffarelli-Kohn-Nirenberg inequality.
基金supported by the National Natural Science Foundation of China(No.11971153)Nanjing University of Aeronautics and Astronautics Research and Practice Innovation Program(No.xcxjh20220802)。
文摘In this paper,the authors study the gradient estimates for positive weak solutions to the following p-Laplacian equation△_(p)u+au^(σ)=0 on complete noncompact Riemannian manifold,where a,σare two nonzero real constants with p≠2.Using the gradient estimate,they can get the corresponding Lionville theorem.On the other hand,by virtue of the Poincare inequality,they also obtain a Liouville theorem under some integral conditions with respect to positive weak solutions.
基金supported by the Laboratories of Excellence(LabEx) NUMEV(solutions Numériques,Matricielles et Modélisation pour l’Environnement et le Vivant)the LabEx CEMEB(Centre Méditerranéen de l’Environnement et de la Biodiversité)the Ecoles Doctorales SIBAGHE and I2S of Montpellier
文摘The goal of this paper is to study the mathematical properties of a new model of soil carbon dynamics which is a reaction-diffusion system with a chemotactic term, with the aim to account for the formation of soil aggregations in the bacterial and microorganism spatial organization(hot spot in soil). This is a spatial and chemotactic version of MOMOS(Modelling Organic changes by Micro-Organisms of Soil), a model recently introduced by M. Pansu and his group. The authors present here two forms of chemotactic terms, first a"classical" one and second a function which prevents the overcrowding of microorganisms.They prove in each case the existence of a nonnegative global solution, and investigate its uniqueness and the existence of a global attractor for all the solutions.
