Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Absence of the Lavrentiev phenomenon for degenerate parabolic double phase problems

Bogi Kim, Youngchae Kim, Jehan Oh

Abstract

We establish the absence of the Lavrentiev phenomenon for degenerate parabolic double phase problems. Any finite-energy function in the natural parabolic class admits smooth approximations with convergence in the parabolic Sobolev space and convergence of the corresponding energy. We provide explicit gap bound conditions and derive improved bounds under additional assumptions such as boundedness or stronger time regularity.

Absence of the Lavrentiev phenomenon for degenerate parabolic double phase problems

Abstract

We establish the absence of the Lavrentiev phenomenon for degenerate parabolic double phase problems. Any finite-energy function in the natural parabolic class admits smooth approximations with convergence in the parabolic Sobolev space and convergence of the corresponding energy. We provide explicit gap bound conditions and derive improved bounds under additional assumptions such as boundedness or stronger time regularity.
Paper Structure (4 sections, 4 theorems, 79 equations)

This paper contains 4 sections, 4 theorems, 79 equations.

Table of Contents

  1. Introduction
  2. Parabolic mollification
  3. Lavrentiev phenomenon without $L^2$-energy term
  4. Lavrentiev phenomenon with $L^2$-energy term

Key Result

Theorem 1.3

Let $\mathcal{P}$ be the functional defined in def : stationary part of the parabolic double phase functional under cond : assumption of w and a. Then the following results hold:

Theorems & Definitions (9)

  • Definition 1.1
  • Remark 1.2
  • Theorem 1.3
  • Theorem 1.4
  • Proposition 2.1
  • proof
  • Proposition 2.2: hasto2025higher, Proposition 4.1
  • proof : Proof of Theorem \ref{['thm: main theorem 1']}
  • proof : Proof of Theorem \ref{['thm: main theorem 2']}