5 papers
Liouville Theorems for the Lane-Emden Equation Involving a Mixed Local-Nonlocal Operator
Yahong Guo, Congming Li, Jiongduo Xie
In this paper, we investigate the existence of positive supersolutions for the following mixed local-nonlocal Lane-Emden type equation: $$ -Δu+(-Δ)^s u=u^q\quad\text{in }\mathbb R^…
Pointwise regularity of solutions for fully fractional parabolic equations
Yahong Guo, Qizhen Shen, Jiongduo Xie
This paper investigates the higher pointwise regularity of nonnegative classical solutions for fully fractional parabolic equations where .…
Global Schauder Regularity and Convergence for Uniformly Degenerate Parabolic Equations
Qing Han, Jiongduo Xie
In this paper, we study the global Hölder regularity of solutions to uniformly degenerate parabolic equations. We also study the convergence of solutions as time goes to infinity u…
Uniformly Degenerate Elliptic Equations with Varying Characteristic Exponents
Qing Han, Jiongduo Xie
In this paper, we study the regularity of solutions to uniformly degenerate elliptic equations in bounded domains under the condition that the characteristic polynomials have varyi…
Optimal Boundary Regularity for Uniformly Degenerate Elliptic Equations
Qing Han, Jiongduo Xie
In this survey paper, we study the optimal regularity of solutions to uniformly degenerate elliptic equations in bounded domains and establish the Hölder continuity of solutions an…