Boundary bubbling analysis of approximate harmonic maps under either weak or strong anchoring conditions in dimension two

TL;DR

This paper investigates the bubbling phenomena of approximate harmonic maps in two dimensions, focusing on cases with either weak or strong anchoring conditions and bounded tension fields.

Contribution

It provides a detailed analysis of bubbling behavior for approximate harmonic maps under different anchoring conditions with bounded tension fields.

Findings

Bubbling phenomena characterized under weak anchoring with bounded $L^2$-tension.

Bubbling behavior analyzed under strong anchoring with bounded $L ext{log}L$ and $M^{1, heta}$-tension fields.

New insights into boundary bubbling phenomena for approximate harmonic maps in dimension two.

Abstract

In this paper, we will study the bubbling phenomena of approximate harmonic maps in dimension two that have either (i) bounded $L^2$-tension fields under the weak anchoring condition, or (ii) bounded $L\log L \cap M^{1,\delta}$-tension fields under the strong anchoring condition.