Estimates on elliptic equations that hold only where the gradient is large

We consider the simplest form of a second order, linear, degenerate, elliptic equation with divergence structure in the plane. Under an integrability condition on the degenerate function, we prove that the solutions are continuous.

The Robbins problem for elliptic equations in space

K. I. Iordanidis (1971)

Δελτίο της Ελληνικής Μαθηματικής Εταιρίας

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Elliptic Carmichael numbers and elliptic Korselt criteria

Joseph H. Silverman (2012)

Acta Arithmetica

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On Two-Dimensional Elliptic Systems with a One-sided Condition.

Michael Wiegner (1981)

Mathematische Zeitschrift

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A Counterexample in Elliptic Regularity Theory.

Michael Struwe (1981)

Manuscripta mathematica

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On fully nonlinear elliptic equations of second order

L. Nirenberg (1988-1989)

Séminaire Équations aux dérivées partielles (Polytechnique)

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On the Green's function for second order elliptic differential equations

B. Szafirski (1967)

Colloquium Mathematicae

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Liouville Theorems for Nondiagonal Elliptic Systems in Arbitrary Dimensions.

Michael Meier (1981)

Mathematische Zeitschrift

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A characterization of elliptic operators

Grzegorz Łysik, Paweł M. Wójcicki (2014)

Annales Polonici Mathematici

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We give a characterization of constant coefficients elliptic operators in terms of estimates of their iterations on smooth functions.