On weak and viscosity solutions of nonlocal double phase equations

Y Fang, C Zhang - International Mathematics Research Notices, 2022 - ieeexplore.ieee.org
We consider the nonlocal double phase equation PV&R^n|u(x)-u(y)|^p-2(u(x)-
u(y))K_sp(x,y)\,dy\&+PVR^na(x,y)|u(x)-u(y)|^q-2(u(x)-u(y))K_tq(x,y)\,dy=0, where 1<p≦q and …

Global regularity for a class of fully nonlinear PDEs with unbalanced variable degeneracy

EC Bezerra Júnior, JV da Silva… - Journal of the …, 2023 - Wiley Online Library
We establish the existence and sharp global regularity results (C 0, γ C^0,γ, C 0, 1 C^0,1
and C 1, α C^1,α estimates) for a class of fully nonlinear elliptic Partial Differential Equations …

Equivalence of weak and viscosity solutions for the nonhomogeneous double phase equation

Y Fang, VD Rădulescu, C Zhang - Mathematische Annalen, 2024 - Springer
We establish the equivalence between weak and viscosity solutions to the
nonhomogeneous double phase equation with lower-order term-div (| D u| p-2 D u+ a (x)| D …

Geometric gradient estimates for fully nonlinear models with non-homogeneous degeneracy and applications

JV da Silva, GC Ricarte - Calculus of Variations and Partial Differential …, 2020 - Springer
We establish sharp C_ loc^ 1, β C loc 1, β geometric regularity estimates for bounded
solutions of a class of fully nonlinear elliptic equations with non-homogeneous degeneracy …

Quasilinear double phase problems in the whole space via perturbation methods

B Ge, P Pucci - Advances in Differential Equations, 2022 - projecteuclid.org
We are concerned with the following double phase problems in the whole space $$\begin
{aligned}-{\rm div}(|\nabla u|^{p-2}\nabla u+ &\mu (x)|\nabla u|^{q-2}\nabla u)\\&+| u|^{p-2} …

Generalized superharmonic functions with strongly nonlinear operator

I Chlebicka, A Zatorska-Goldstein - Potential Analysis, 2022 - Springer
We study properties of A A-harmonic and A A-superharmonic functions involving an operator
having generalized Orlicz growth. Our framework embraces reflexive Orlicz spaces, as well …

Regularity for quasi-linear parabolic equations with nonhomogeneous degeneracy or singularity

Y Fang, C Zhang - Calculus of Variations and Partial Differential …, 2023 - Springer
We introduce a new class of quasi-linear parabolic equations involving nonhomogeneous
degeneracy or/and singularity∂ tu=[| D u| q+ a (x, t)| D u| s] Δ u+(p-2) D 2 u Du| D u|, Du| D …

Asymptotic mean value properties for the elliptic and parabolic double phase equations

W Meng, C Zhang - Nonlinear Differential Equations and Applications …, 2023 - Springer
We characterize an asymptotic mean value formula in the viscosity sense for the double
phase elliptic equation-div (|∇ u| p-2∇ u+ a (x)|∇ u| q-2∇ u)= 0 and the normalized double …

Regularity for Double Phase Functionals with Two Modulating Coefficients

B Kim, J Oh - The Journal of Geometric Analysis, 2024 - Springer
In this paper, we establish regularity results for local minimizers of functionals with non-
standard growth conditions and non-uniform ellipticity properties. The model case is given …

Weak differentiability to nonuniform nonlinear degenerate elliptic systems under p, q-growth condition on the Heisenberg group

J Zhang, Z Li - Journal of Mathematical Analysis and Applications, 2023 - Elsevier
The paper concerns the weak differentiability of weak solutions to two kinds of nonuniform
nonlinear degenerate elliptic systems under the p, q-growth condition on the Heisenberg …