Partial regularity and higher integrability for A-quasiconvex variational problems

2024/12/13 by Zhuolin Li, Li, Zhuolin, Bogdan Raiţă +1
Computer Science · Mathematics · #Optimization and Variational Analysis #Contact Mechanics and Variational Inequalities #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2412.10363

Abstract

We prove that minimizers of variational problems on open sets Ω⊂ ℝⁿ minimize \mathcal E(v)=∫_Ωf(v(x))d x\quadfor \mathscrA v=0, are partially continuous provided that the integrands f are strongly \mathscrA-quasiconvex in a suitable sense. We consider p-growth problems with 1

Related

• Partial Regularity for \mathbbA-quasiconvex Functionals
• Partial regularity for minimizers of quasiconvex functionals with general growth
• Partial regularity for minimizers of discontinuous quasiconvex integrals with general growth
• Regularity for higher order quasiconvex problems with linear growth from below
• Partial regularity for ω-minimizers of quasiconvex functionals