Interior continuity, continuity up to the boundary, and Harnack's inequality for double‐phase elliptic equations with nonlogarithmic conditions
From MaRDI portal
Publication:6073225
DOI10.1002/mana.202000574arXiv2012.10960OpenAlexW3116328001MaRDI QIDQ6073225
Unnamed Author, Unnamed Author, Igor I. Skrypnik
Publication date: 17 October 2023
Published in: Mathematische Nachrichten (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2012.10960
Harnack's inequalitycontinuity of solutionsregularity of a boundary pointdouble-phase elliptic equationsnonlogarithmic conditions
Smoothness and regularity of solutions to PDEs (35B65) Regularity of solutions in optimal control (49N60) Weak solutions to PDEs (35D30) Quasilinear elliptic equations with (p)-Laplacian (35J92)
Related Items
Regularity theory for non-autonomous problems with a priori assumptions ⋮ Harnack inequality for solutions of the \(p(x)\)-Laplace equation under the precise non-logarithmic Zhikov's conditions ⋮ Recent developments in problems with nonstandard growth and nonuniform ellipticity
Cites Work
- Bounded minimisers of double phase variational integrals
- Hölder regularity of quasiminimizers under generalized growth conditions
- Lebesgue and Sobolev spaces with variable exponents
- On the continuity of solutions to elliptic equations with variable order of nonlinearity
- The weak Harnack inequality for unbounded supersolutions of equations with generalized Orlicz growth
- Calderón-Zygmund estimates and non-uniformly elliptic operators
- Regularity of minimizers of integrals of the calculus of variations with non-standard growth conditions
- On Lavrentiev's phenomenon
- On some variational problems
- Boundary regularity under generalized growth conditions
- Orlicz spaces and generalized Orlicz spaces
- Regularity for general functionals with double phase
- Local continuity and Harnack's inequality for double-phase parabolic equations
- \( \mathcal{B}_1\) classes of De Giorgi-Ladyzhenskaya-Ural'tseva and their applications to elliptic and parabolic equations with generalized Orlicz growth conditions
- Regularity for double phase variational problems
- Harnack's inequality for the \(p(x)\)-Laplacian with a two-phase exponent \(p(x)\)
- Regularity for double phase problems under additional integrability assumptions
- Harnack inequalities for double phase functionals
- Pointwise estimates of solutions to \(2 m\)-order quasilinear elliptic equations with \(m(p, q)\) growth via Wolff potentials
- On the density of smooth functions in Sobolev-Orlicz spaces
- Regularity and existence of solutions of elliptic equations with p,q- growth conditions
- Non-autonomous functionals, borderline cases and related function classes
- Improved integrability of the gradients of solutions of elliptic equations with variable nonlinearity exponent
- A class of De Giorgi type and Hölder continuity
- A Harnack inequality for a transmission problem withp(x)-Laplacian
- The natural generalizationj of the natural conditions of ladyzhenskaya and uralľtseva for elliptic equations
- Harnack's inequality for quasilinear elliptic equations with generalized Orlicz growth
- Hölder continuity of $\omega$-minimizers of functionals with generalized Orlicz growth
- Behavior of solutions of the Dirichlet Problem for the $p(x)$-Laplacian at a boundary point
- SOME PROBLEMS OF THE QUALITATIVE THEORY OF SECOND ORDER ELLIPTIC EQUATIONS (CASE OF SEVERAL INDEPENDENT VARIABLES)
- Continuity at boundary points of solutions of quasilinear elliptic equations with a non-standard growth condition
- Hölder continuity of $ p(x)$-harmonic functions
- Energy methods for free boundary problems. Applications to nonlinear PDEs and fluid mechanics
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item