Regularity results for minimizers of \((2,q)\)-growth functionals in the Heisenberg group

DOI10.1007/S00229-010-0366-0zbMath1203.35057OpenAlexW2008007935MaRDI QIDQ993396

Anna Föglein

Publication date: 10 September 2010

Published in: Manuscripta Mathematica (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00229-010-0366-0

zbMATH Keywords

growth of order \(q>2\) from abovequadratic growth from below

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Regularity of solutions in optimal control (49N60) Subelliptic equations (35H20) PDEs on Heisenberg groups, Lie groups, Carnot groups, etc. (35R03)

Related Items (2)

Local boundedness of variational solutions to evolutionary problems with non-standard growth ⋮ Recent developments in problems with nonstandard growth and nonuniform ellipticity

Cites Work

• Unnamed Item
• Unnamed Item
• Embedding theorems into Lipschitz and BMO spaces and applications to quasilinear subelliptic differential equations
• Regularity for elliptic equations with general growth conditions
• Regularity of relaxed minimizers of quasiconvex variational integrals with \((p, q)\)-growth
• Regularity of minima: an invitation to the dark side of the calculus of variations.
• Nonlinear subelliptic equations
• Gradient bounds for the horizontal \(p\)-Laplacian on a Carnot group and some applications
• On the definition and the lower semicontinuity of certain quasiconvex integrals
• Growth conditions and regularity. A counterexample
• Regularity of minimizers of integrals of the calculus of variations with non-standard growth conditions
• Regularity for minima of functionals with p-growth
• Hölder continuity of minimizers of functionals with non standard growth conditions
• Subelliptic estimates and function spaces on nilpotent Lie groups
• Regularity for quasilinear equations and 1-quasiconformal maps in Carnot groups
• Higher differentiability for weak solutions of elliptic systems with nonstandard growth conditions
• Higher integrability for minimizers of integral functionals with nonstandard growth
• Regularity of minimizers of the calculus of variations in Carnot groups via hypoellipticity of systems of Hörmander type
• Higher integrability for minimizers of integral functionals with \((p,q)\) growth
• The Poincaré inequality for vector fields satisfying Hörmander's condition
• Regularity results for stationary electro-rheological fluids
• Sharp regularity for functionals with (\(p\),\(q\)) growth
• Differentiability of solutions for the non-degenerate \(p\)-Laplacian in the Heisenberg group
• Weighted Poincaré and Sobolev inequalities for vector fields satisfying Hörmander's condition and applications
• Gradient regularity for elliptic equations in the Heisenberg group
• Regularity results for quasilinear elliptic equations in the Heisenberg group
• Partial regularity results for subelliptic systems in the Heisenberg group
• Hypoelliptic second order differential equations
• Regularity for some scalar variational problems under general growth conditions
• Regularity and existence of solutions of elliptic equations with p,q- growth conditions
• Regularity results for minimizers of irregular integrals with (p,q) growth
• Subelliptic Cordes estimates
• An embedding theorem and the harnack inequality for nonlinear subelliptic equations
• Local boundedness of minimizers of certain degenerate functionals of the calculus of variations
• Regularity of quasi-linear equations in the Heisenberg group
• Gradient estimates for thep(x)-Laplacean system
• Regularity results for a class of functionals with non-standard growth
• \(C^{1,\alpha}\) local regularity for the solutions of the \(p\)-Laplacian on the Heisenberg group for \(2 \leq p < 1 + \sqrt{5}\)

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