Scholarlink

<p>Mainly motivated by the mirror symmetry considerations, we investigate the Dirichlet problem for the Lagrangian phase operator with <i>supercritical</i> phase on a general almost complex manifold <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\((M,J,\omega )\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">(</mo> <mi>M</mi> <mo>,</mo> <mi>J</mi> <mo>,</mo> <mi>ω</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation>. Under the key assumption of smooth subsolution existence, we establish a priori <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(C^{2,\alpha }\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>C</mi> <mrow> <mn>2</mn> <mo>,</mo> <mi>α</mi> </mrow> </msup> </math></EquationSource> </InlineEquation> estimates for solutions to this nonlinear elliptic equation. Building on these regularity results, we resolve the Dirichlet problem by proving the existence and uniqueness of smooth solutions.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

The Dirichlet Problem for Complex Lagrangian Operator on Almost Complex Manifolds

  • 期刊论文

  • 发表日期：

    2026年8月1日

查看全文
  • Jiaogen Zhang

摘要

Mainly motivated by the mirror symmetry considerations, we investigate the Dirichlet problem for the Lagrangian phase operator with supercritical phase on a general almost complex manifold \((M,J,\omega )\) ( M , J , ω ) . Under the key assumption of smooth subsolution existence, we establish a priori \(C^{2,\alpha }\) C 2 , α estimates for solutions to this nonlinear elliptic equation. Building on these regularity results, we resolve the Dirichlet problem by proving the existence and uniqueness of smooth solutions.