We consider, for a bounded open domain Ω in <em>R<sup>n</sup></em> and a function <em>u</em> : Ω → <em>R<sup>m</sup></em>, the quasilinear elliptic system...We consider, for a bounded open domain Ω in <em>R<sup>n</sup></em> and a function <em>u</em> : Ω → <em>R<sup>m</sup></em>, the quasilinear elliptic system: <img src="Edit_8a3d3105-dccb-405b-bbbc-2084b80b6def.bmp" alt="" /> (1). We generalize the system (<em>QES</em>)<sub>(<em>f</em>,<em>g</em>)</sub> in considering a right hand side depending on the jacobian matrix <em>Du</em>. Here, the star in (<em>QES</em>)<sub>(<em>f</em>,<em>g</em>)</sub> indicates that <em>f </em>may depend on <em>Du</em>. In the right hand side, <em>v</em> belongs to the dual space <em>W</em><sup>-1,<em>P</em>’</sup>(Ω, <span style="white-space:nowrap;"><em>ω</em></span><sup>*</sup>,<em> R<sup>m</sup></em>), <img src="Edit_d584a286-6ceb-420c-b91f-d67f3d06d289.bmp" alt="" />, <em>f </em>and <em>g</em> satisfy some standard continuity and growth conditions. We prove existence of a regularity, growth and coercivity conditions for <em>σ</em>, but with only very mild monotonicity assumptions.展开更多
Using the theory of weighted Sobolev spaces with variable exponent and the <em>L</em><sup>1</sup>-version on Minty’s lemma, we investigate the existence of solutions for some nonhomogeneous Di...Using the theory of weighted Sobolev spaces with variable exponent and the <em>L</em><sup>1</sup>-version on Minty’s lemma, we investigate the existence of solutions for some nonhomogeneous Dirichlet problems generated by the Leray-Lions operator of divergence form, with right-hand side measure. Among the interest of this article is the given of a very important approach to ensure the existence of a weak solution of this type of problem and of generalization to a system with the minimum of conditions.展开更多
文摘We consider, for a bounded open domain Ω in <em>R<sup>n</sup></em> and a function <em>u</em> : Ω → <em>R<sup>m</sup></em>, the quasilinear elliptic system: <img src="Edit_8a3d3105-dccb-405b-bbbc-2084b80b6def.bmp" alt="" /> (1). We generalize the system (<em>QES</em>)<sub>(<em>f</em>,<em>g</em>)</sub> in considering a right hand side depending on the jacobian matrix <em>Du</em>. Here, the star in (<em>QES</em>)<sub>(<em>f</em>,<em>g</em>)</sub> indicates that <em>f </em>may depend on <em>Du</em>. In the right hand side, <em>v</em> belongs to the dual space <em>W</em><sup>-1,<em>P</em>’</sup>(Ω, <span style="white-space:nowrap;"><em>ω</em></span><sup>*</sup>,<em> R<sup>m</sup></em>), <img src="Edit_d584a286-6ceb-420c-b91f-d67f3d06d289.bmp" alt="" />, <em>f </em>and <em>g</em> satisfy some standard continuity and growth conditions. We prove existence of a regularity, growth and coercivity conditions for <em>σ</em>, but with only very mild monotonicity assumptions.
文摘Using the theory of weighted Sobolev spaces with variable exponent and the <em>L</em><sup>1</sup>-version on Minty’s lemma, we investigate the existence of solutions for some nonhomogeneous Dirichlet problems generated by the Leray-Lions operator of divergence form, with right-hand side measure. Among the interest of this article is the given of a very important approach to ensure the existence of a weak solution of this type of problem and of generalization to a system with the minimum of conditions.
