In this paper we establish an interior regularity of weak solution for quasi-linear degenerate elliptic equations under the subcritical growth if its coefficient matrix A（x, u） satisfies a VMO condition in the varia...In this paper we establish an interior regularity of weak solution for quasi-linear degenerate elliptic equations under the subcritical growth if its coefficient matrix A（x, u） satisfies a VMO condition in the variable x uniformly with respect to all u, and the lower order item B（x, u, △↓u） satisfies the subcritical growth （1.2）. In particular, when F（x） ∈ L^q（Ω） and f（x） ∈ L^γ（Ω） with q,γ 〉 for any 1 〈 p 〈 ＋∞, we obtain interior HSlder continuity of any weak solution of （1.1） u with an index κ = min{1 - n/q, 1 - n/γ}.展开更多
This paper is devoted to the functional analytic approach to the problem of the existence of Markov processes in probability theory. More precisely, we construct Feller semigroups with Dirichlet conditions for second-...This paper is devoted to the functional analytic approach to the problem of the existence of Markov processes in probability theory. More precisely, we construct Feller semigroups with Dirichlet conditions for second-order, uniformly elliptic integro-differential operators with discontinuous coefficients. In other words, we prove that there exists a Feller semigroup corresponding to such a diffusion phenomenon that a Markovian particle moves both by jumps and continuously in the state space until it dies at the time when it reaches the boundary.展开更多
基金National Natural Science Foundation of China (No.10671022)
文摘In this paper we establish an interior regularity of weak solution for quasi-linear degenerate elliptic equations under the subcritical growth if its coefficient matrix A（x, u） satisfies a VMO condition in the variable x uniformly with respect to all u, and the lower order item B（x, u, △↓u） satisfies the subcritical growth （1.2）. In particular, when F（x） ∈ L^q（Ω） and f（x） ∈ L^γ（Ω） with q,γ 〉 for any 1 〈 p 〈 ＋∞, we obtain interior HSlder continuity of any weak solution of （1.1） u with an index κ = min{1 - n/q, 1 - n/γ}.
基金Supported in part by Grant-in-Aid for General Scientific Research (No. 16340031)Ministry of Education,Culture, Sports, Science and Technology, Japan
文摘This paper is devoted to the functional analytic approach to the problem of the existence of Markov processes in probability theory. More precisely, we construct Feller semigroups with Dirichlet conditions for second-order, uniformly elliptic integro-differential operators with discontinuous coefficients. In other words, we prove that there exists a Feller semigroup corresponding to such a diffusion phenomenon that a Markovian particle moves both by jumps and continuously in the state space until it dies at the time when it reaches the boundary.
