Abstract
We present new regularity result in the study of elliptic equations with mixed boundary conditions. We obtain small higher integrability of the gradient (Meyers property). The result is new for both linear and nonlinear equations with degenerate coefficients with a new sharp Maz’ya-type capacity condition on the part with Dirichlet boundary condition, while prior research was limited to uniformly elliptic weights.
Funding source: Deutsche Forschungsgemeinschaft
Award Identifier / Grant number: SFB 1283/2 2021 – 317210226
Award Identifier / Grant number: GRK 2235/2 2021 – 282638148
Funding statement: Anna Kh. Balci is funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) – SFB 1283/2 2021 – 317210226, Charles University in Prague PRIMUS/24/SCI/020 and Research Centre program No. UNCE/24/SCI/005. Ho-Sik Lee is funded by Deutsche Forschungsgemeinschaft through GRK 2235/2 2021 – 282638148.
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Articles in the same Issue
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- A characterization of ℓ1 double bubbles with general interface interaction
- The weak Harnack inequality for unbounded minimizers of elliptic functionals with generalized Orlicz growth
- On the behavior in time of the solutions to total variation flow
- Zaremba problem with degenerate weights
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- Struwe’s global compactness and energy approximation of the critical Sobolev embedding in the Heisenberg group
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Articles in the same Issue
- Frontmatter
- A characterization of ℓ1 double bubbles with general interface interaction
- The weak Harnack inequality for unbounded minimizers of elliptic functionals with generalized Orlicz growth
- On the behavior in time of the solutions to total variation flow
- Zaremba problem with degenerate weights
- Point-wise characterizations of limits of planar Sobolev homeomorphisms and their quasi-monotonicity
- Struwe’s global compactness and energy approximation of the critical Sobolev embedding in the Heisenberg group
- On the variational nature of the Anzellotti pairing
- Strongly nonlinear Robin problems for harmonic and polyharmonic functions in the half-space
- Upper semicontinuity of index plus nullity for minimal and CMC hypersurfaces
- A variational approach to the Navier–Stokes equations with shear-dependent viscosity
- Hölder regularity for the fractional p-Laplacian, revisited
- Poincaré inequality and energy of separating sets
- On a class of obstacle problems with (p, q)-growth and explicit u-dependence
- Stepanov differentiability theorem for intrinsic graphs in Heisenberg groups
- Parabolic Lipschitz truncation for multi-phase problems: The degenerate case