Second-Order Two-Sided Estimates in Nonlinear Elliptic Problems
By Andrea Cianchi, Vladimir G. Maz'ya. 2017
110 citations recorded by the source corpus.
Best possible second-order regularity is established for solutions to p-Laplacian type equations with $${p \in (1, \infty)}$$p∈(1,∞) and a square-integrable right-hand side. Our results provide a nonlinear counterpart of the classical L2-coercivity theory for linear problems, which is missing in the existing literature. Both local and global estimates are obtained. The latter apply to solutions to either Dirichlet or Neumann boundary value problems. Minimal regularity on the boundary of the domain is required, although our conclusions are new even for smooth domains. If the domain is convex, no regularity of its boundary is needed at all.
Subfields: Applied Mathematics, Computational Theory and Mathematics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/f6155e6d8ba44567371e0b48486ae4aacf494bf9
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In Applied Mathematics
- Giulio Ciraolo
- Alessio Figalli
- A. Roncoroni
- Iwona Chlebicka
- Alberto Farina
- C. Antonini
- Guido De Philippis
- Max Fathi
In Computational Theory and Mathematics
- Giulio Ciraolo
- A. Roncoroni
- Iwona Chlebicka
- Alberto Farina
- Alessio Figalli
- C. Antonini
- Paolo Marcellini
- Enrico Valdinoci
In Mathematical Physics
- Giulio Ciraolo
- A. Roncoroni
- Iwona Chlebicka
- Alberto Farina
- Alessio Figalli
- C. Antonini
- Paolo Marcellini
Citations in the corpus
- Interior regularity results for inhomogeneous anisotropic quasilinear equations (2021, methodology): “In [6] an equation driven by a rotationally-invariant operator is considered, i.”
- Symmetry results for critical anisotropic p-Laplacian equations in convex cones (2019, methodology): “p−1 ∀r≥ 1, (2.38) where Cis a positive constant independent of r. Proof. The estimate (2.38) is obtained by using a Caccioppoli-type inequality. We argue by approximation, following the approach in [3, 11]. 12 GIULIO CIRAOLO, ALESSIO FIGALLI, AND ALBERTO RONCORONI We approximate Σ by a sequence of ”
- A pocket guide to nonlinear differential equations in Musielak–Orlicz spaces (2018, background): “26, 81, 92, 112, 113, 117, 141, 147]. Note that [24, 195] concern isotropic variable exponent spaces, while [22, 23, 141] the anisotropic 20 ones. Isotropic and reflexive Orlicz spaces are employed in [7, 26, 60, 61, 80], isotropic and nonreflexive in [46], while anisotropic and nonreflexive ones in [1”