Compactness methods for Hölder estimates of certain degenerate elliptic equations

In this paper we obtain the interior $C^{1,\alpha}$ regularity of the quasilinear elliptic equations of divergence form. Our basic tools are the elementary local $L^\infty$ estimates and weak Harnack inequality for second-order linear elliptic equations, and the compactness method

Characterization of Ferroelectric Na x K 1Àx NbO 3 System Films Prepared by Pulsed Laser Deposition

Ferroelectric Na x K 1Àx NbO 3 (NKN) films were prepared on quartz and Pt/SrTiO 3 (100) substrates by pulsed laser deposition. The effects of composition and preparation conditions on the crystal structure and ferroelectricity of the NKN films were investigated by changing the Na content (x), substrate temperature (T sub ), oxygen partial pressure (P O2 ), target-to-substrate distance (D t-s ) and laser energy density (E L ). The permittivity values of the NKN films were 390 to 520 at room temperature and 100 kHz, showing a maximum at x ¼ 0:5. The maximum remnant polarization value was 8:2 Â 10 À2 C m À2 at x ¼ 0:5

Compactness methods for Hölder estimates of certain degenerate elliptic equations

In this paper we obtain the interior $C^{1,\alpha}$ regularity of the quasilinear elliptic equations of divergence form. Our basic tools are the elementary local $L^\infty$ estimates and weak Harnack inequality for second-order linear elliptic equations, and the compactness method