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Regularity of Solutions to a Class of Degenerate Cross Diffusion Systems of $m$ Equations

Dung Le

Abstract

We study the regularity of weak solutions and the global existence of classical to cross-diffusion systems of $m$ equations on $N$-dimensional domains ($m,N\ge2$).

Regularity of Solutions to a Class of Degenerate Cross Diffusion Systems of $m$ Equations

Abstract

We study the regularity of weak solutions and the global existence of classical to cross-diffusion systems of equations on -dimensional domains ().
Paper Structure (6 sections, 9 theorems, 61 equations)

This paper contains 6 sections, 9 theorems, 61 equations.

Table of Contents

  1. Introduction
  2. Weighted Gagliardo-Nirenberg inequalities involving BMO norms
  3. The sketch of the proof for the weighted strong Gagliardo-Nirenberg inequality with BMO norms:
  4. A new (weak) weighted Gagliardo-Nirenberg inequality
  5. Regularity for degenerate systems:
  6. Uniqueness of weak solutions

Key Result

Theorem 2.1

Suppose that $\varepsilon_0(R),I_1,I_2,\breve{{\mathcal{I}}}_0$ are finite and that there is a constant $C_*(R)$ such that Define $\varepsilon_0(R) =\|u\|_{BMO(\Omega_{2R})}$. Then, there are constants $C(N), C(N,p)$ such that

Theorems & Definitions (19)

  • Theorem 2.1
  • Remark 2.2
  • Remark 2.3
  • Remark 2.4
  • Theorem 2.5
  • Theorem 3.1
  • Remark 3.2
  • Remark 3.3
  • Remark 3.4
  • Corollary 3.5
  • ...and 9 more