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We investigate the regularity of the weak solution to elliptic transmission problems that involve two layered anisotropic materials separated by a boundary intersecting interface. Under a pair of compatibility conditions for the angle of the two surfaces and the boundary data at the contact line, we prove the existence of up to the boundary square-integrable second derivatives, and the global Lipschitz continuity of the solution. If only the weakest, necessary condition is satisfied, we show that...

Global maximal estimates for solutions to the Schrödinger equation

Per Sjölin (1994)

Studia Mathematica

Global maximal estimates are considered for solutions to an initial value problem for the Schrödinger equation.

Global minimizers for the Ginzburg-Landau functional below the first critical magnetic field

Etienne Sandier, Sylvia Serfaty (2000)

Annales de l'I.H.P. Analyse non linéaire

Global Regularity of Solutions of Nonlinear Second Order Elliptic and Parabolic Differential Equations.

Gary M. Liebermann (1986)

Mathematische Zeitschrift

Global regularity of the solutions to the capillarity problem

Claus Gerhardt (1976)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Global Schauder estimates for a class of degenerate Kolmogorov equations

Enrico Priola (2009)

Studia Mathematica

We consider a class of possibly degenerate second order elliptic operators on ℝⁿ. This class includes hypoelliptic Ornstein-Uhlenbeck type operators having an additional first order term with unbounded coefficients. We establish global Schauder estimates in Hölder spaces both for elliptic equations and for parabolic Cauchy problems involving . The Hölder spaces in question are defined with respect to a possibly non-Euclidean metric related to the operator . Schauder estimates are deduced by sharp...

Global solution of optimal shape design problems.

Fakharzadeh J., A., Rubio, J.E. (1999)

Zeitschrift für Analysis und ihre Anwendungen

Global solutions of the homogeneous complex Monge-Ampère equation and complex structures on the tangent bundle of Riemannian manifolds.

László Lempert, Róbert Szöke (1991)

Mathematische Annalen

Global weak solutions of the Navier-Stokes equations with nonhomogeneous boundary data and divergence

R. Farwig, H. Kozono, H. Sohr (2011)

Rendiconti del Seminario Matematico della Università di Padova

Gluing approximate solutions of minimum type on the Nehari manifold.

Li, Yanyan, Wang, Zhi-Qiang (2001)

Electronic Journal of Differential Equations (EJDE) [electronic only]

Gradient bounds and Liouville theorems for quasilinear elliptic equations

L. A. Peletier, J. Serrin (1978)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Gradient estimates for a new class of degenerate elliptic and parabolic equations

Gary M. Lieberman (1994)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Gradient estimates for a nonlinear equation $Δ_{f} u + c u^{- α} = 0$ on complete noncompact manifolds

Jing Zhang, Bingqing Ma (2011)

Communications in Mathematics

Let $(M, g)$ be a complete noncompact Riemannian manifold. We consider gradient estimates on positive solutions to the following nonlinear equation $Δ_{f} u + c u^{- α} = 0$ in $M$ , where $α$ , $c$ are two real constants and $α > 0$ , $f$ is a smooth real valued function on $M$ and $Δ_{f} = Δ - \nabla f \nabla$ . When $N$ is finite and the $N$ -Bakry-Emery Ricci tensor is bounded from below, we obtain a gradient estimate for positive solutions of the above equation. Moreover, under the assumption that $\infty$ -Bakry-Emery Ricci tensor is bounded from below and $| \nabla f |$ is bounded from above,...

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