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<p>In this work we study a priori bounds for weak solution to elliptic problems with nonstandard growth that involves the so-called <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(g-\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>g</mi> <mo>-</mo> </mrow> </math></EquationSource> </InlineEquation>Laplace operator. The <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(g-\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>g</mi> <mo>-</mo> </mrow> </math></EquationSource> </InlineEquation>Laplacian is a generalization of the <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(p-\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>p</mi> <mo>-</mo> </mrow> </math></EquationSource> </InlineEquation>Laplace operator that takes into account different behaviors than pure powers. The method to obtain these a priori estimates is the so called “blow-up” argument developed by Gidas and Spruck. Then we applied this a priori bounds to show some existence results for these problems.</p>

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A priori estimates for solutions of g-Laplace type problems

  • 期刊论文

  • 发表日期：

    2026年7月9日

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  • Ignacio Ceresa Dussel,
  • Julián Fernández Bonder,
  • Analía Silva

摘要

In this work we study a priori bounds for weak solution to elliptic problems with nonstandard growth that involves the so-called \(g-\) g - Laplace operator. The \(g-\) g - Laplacian is a generalization of the \(p-\) p - Laplace operator that takes into account different behaviors than pure powers. The method to obtain these a priori estimates is the so called “blow-up” argument developed by Gidas and Spruck. Then we applied this a priori bounds to show some existence results for these problems.