JournalsaihpcVol. 6, No. 5pp. 347–361

Univalent solutions of elliptic systems of Heinz-Lewy type

  • Friedmar Schulz

    Department of Mathematics, The University of Iowa, Iowa City, IA 52242, U.S.A.
Univalent solutions of elliptic systems of Heinz-Lewy type cover
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Abstract

Under consideration are homeomorphisms u = (u1(x1, x2), u2(x1, x2)) with finite Dirichlet integral which solve binary, quasilinear elliptic systems (3) with quadratic growth in the gradient of the solution mapping. Regularity results are derived under minimal assumptions on the coefficients of the system. The non-vanishing of the Jacobian is shown for the Heinz-Lewy system (1) together with an a priori estimate from below under suitable normalizations. This involves proving an asymptotic expansion for real-valued functions φ(x) satisfying the differential inequality (2).

Résumé

On considére des homéomorphismes u = (u1(x1, x2), u2(x1, x2)) dont l’intégrale de Dirichlet est finie et qui résolvent certains systèmes elliptiques quasilinéaires. On démontre alors des résultats de régulants. Dans le cas particulier du système des Heinz-Lewy, on démontre la non-nullité du Jacobien ainsi qu’une estimation a priori par le dessous.

Cite this article

Friedmar Schulz, Univalent solutions of elliptic systems of Heinz-Lewy type. Ann. Inst. H. Poincaré Anal. Non Linéaire 6 (1989), no. 5, pp. 347–361

DOI 10.1016/S0294-1449(16)30315-8