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<p>This paper extends recent existence results to a more general nonhomogeneous quasilinear elliptic differential equation with variable exponent growth and convection term. The equation has nonvariational structure due to the dependence on the gradient of the unknown function. Our approach relies on pseudomonotone operator theory. Moreover, an <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(L^{\infty }\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>L</mi> <mi>∞</mi> </msup> </math></EquationSource> </InlineEquation>-boundedness result and <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(C^{1,\gamma }\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>C</mi> <mrow> <mn>1</mn> <mo>,</mo> <mi>γ</mi> </mrow> </msup> </math></EquationSource> </InlineEquation>-regularity of the solutions are obtained.</p>

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Solutions to a nonhomogeneous quasilinear elliptic equation with variable exponent growth and convection term

  • 期刊论文

  • 发表日期：

    2026年3月19日

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  • Lotfi Riahi

摘要

This paper extends recent existence results to a more general nonhomogeneous quasilinear elliptic differential equation with variable exponent growth and convection term. The equation has nonvariational structure due to the dependence on the gradient of the unknown function. Our approach relies on pseudomonotone operator theory. Moreover, an \(L^{\infty }\) L ∞ -boundedness result and \(C^{1,\gamma }\) C 1 , γ -regularity of the solutions are obtained.