Higher order Poincaré inequality and Caccioppoli inequality with Orlicz norms for differential forms

Nonlinear elliptic equations (35J60) A priori estimates in context of PDEs (35B45) Inequalities for sums, series and integrals (26D15) Exterior differential systems (Cartan theory) (58A15)

Cites Work

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Higher integrability of Green's operator and homotopy operator
Higher integrability of iterated operators on differential forms
\(W^{1,p}\)-quasiconvexity and variational problems for multiple integrals
Convexity conditions and existence theorems in nonlinear elasticity
Hardy-Littlewood theorems for \(A\)-harmonic tensors
Integral estimates for null Lagrangians
Higher order Poincaré inequalities associated with linear operators on stratified groups and applications
Hölder estimates and regularity for holomorphic and harmonic functions
Polynomials, higher order Sobolev extension theorems and interpolation inequalities on weighted Folland-Stein spaces on stratified groups
The higher integrability of commutators of Calderón-Zygmund singular integral operators on differential forms
Global Poincaré inequalities for Green's operator applied to the solutions of the nonhomogeneous \(A\)-harmonic equation
Weighted Poincaré inequalities for solutions to \(A\)-harmonic equations.
\(A_{r}^{\lambda}(\Omega)\)-weighted imbedding inequalities for \(A\)-harmonic tensors.
Weighted integral inequalities for solutions of the \(A\)-harmonic equation
Dirac-harmonic equations for differential forms
Poincaré inequalities and the sharp maximal inequalities with \(L^{\varphi}\)-norms for differential forms
Two-weight Poincaré-type inequalities for differential forms in \(L^s(\mu )\)-averaging domains
The L\(^p\)-integrability of the partial derivatives of a quasiconformal mapping
Weighted Poincaré-type estimates for conjugate \(A\)-harmonic tensors
High order representation formulas and embedding theorems on stratified groups and generalizations
Inequalities for Differential Forms
On the Holder Continuity of Quasi Conformal and Elliptic Mappings
Higher integrability of the gradient of minimizers of functional with nonstandard growth conditions
Caccioppoli inequalities with Orlicz norms for solutions of harmonic equations and applications
Two-weight Caccioppoli inequalities for solutions of nonhomogeneous 𝐴-harmonic equations on Riemannian manifolds

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