SOME DIFFERENTIABILITY PROPERTIES OF SOLUTIONS OF ELLIPTIC EQUATIONS WITH MEASURABLE COEFFICIENTS

Mathematics of the USSR-Izvestiya ◽

10.1070/im1986v027n03abeh001205 ◽

1986 ◽

Vol 27 (3) ◽

pp. 601-606

Author(s):

N S Nadirashvili

Keyword(s):

Elliptic Equations ◽

Measurable Coefficients ◽

Differentiability Properties

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UNIMPROVABILITY OF ESTIMATES OF HÖLDER CONSTANTS FOR SOLUTIONS OF LINEAR ELLIPTIC EQUATIONS WITH MEASURABLE COEFFICIENTS

Mathematics of the USSR-Sbornik ◽

10.1070/sm1988v060n01abeh003167 ◽

1988 ◽

Vol 60 (1) ◽

pp. 269-281 ◽

Author(s):

M V Safonov

Keyword(s):

Elliptic Equations ◽

Measurable Coefficients

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On the existence of smooth solutions for fully nonlinear elliptic equations with measurable “coefficients” without convexity assumptions

Methods and Applications of Analysis ◽

10.4310/maa.2012.v19.n2.a2 ◽

2012 ◽

Vol 19 (2) ◽

pp. 119-146

Author(s):

Nicolai V. Krylov

Keyword(s):

Elliptic Equations ◽

Nonlinear Elliptic Equations ◽

Smooth Solutions ◽

Fully Nonlinear Elliptic Equations ◽

Fully Nonlinear ◽

Measurable Coefficients ◽

Nonlinear Elliptic ◽

Convexity Assumptions

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Mixed boundary value problems for nonlinear elliptic equations of second order with measurable coefficients in high dimensional domains

Complex Variables and Elliptic Equations ◽

10.1080/17476930500463887 ◽

2006 ◽

Vol 51 (3) ◽

pp. 267-276

Author(s):

Guo Chun Wen ◽

DeChang Chen

Keyword(s):

Boundary Value Problems ◽

Elliptic Equations ◽

Mixed Boundary ◽

Boundary Value ◽

Nonlinear Elliptic Equations ◽

Second Order ◽

High Dimensional ◽

Mixed Boundary Value Problems ◽

Measurable Coefficients ◽

Nonlinear Elliptic

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Oblique derivative boundary value problems for nonlinear elliptic equations of second order with measurable coefficients in high dimensional domains

Communications in Nonlinear Science and Numerical Simulation ◽

10.1016/j.cnsns.2003.04.002 ◽

2005 ◽

Vol 10 (5) ◽

pp. 559-570 ◽

Author(s):

Guochun Wen ◽

Dechang Chen

Keyword(s):

Boundary Value Problems ◽

Elliptic Equations ◽

Boundary Value ◽

Nonlinear Elliptic Equations ◽

Second Order ◽

High Dimensional ◽

Measurable Coefficients ◽

Nonlinear Elliptic

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Boundary value problems for nonuniformly elliptic equations with measurable coefficients

Annali di Matematica Pura ed Applicata (1923 -) ◽

10.1007/bf02418007 ◽

1976 ◽

Vol 110 (1) ◽

pp. 223-245 ◽

Author(s):

C. V. Coffman ◽

M. M. Marcus ◽

V. J. Mizel

Keyword(s):

Boundary Value Problems ◽

Elliptic Equations ◽

Boundary Value ◽

Measurable Coefficients

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Elliptic equations with measurable coefficients in Reifenberg domains

Advances in Mathematics ◽

10.1016/j.aim.2010.05.014 ◽

2010 ◽

Vol 225 (5) ◽

pp. 2648-2673 ◽

Author(s):

Sun-Sig Byun ◽

Lihe Wang

Keyword(s):

Elliptic Equations ◽

Measurable Coefficients

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Nonuniqueness for Second-Order Elliptic Equations with Measurable Coefficients

SIAM Journal on Mathematical Analysis ◽

10.1137/s0036141096309046 ◽

1999 ◽

Vol 30 (4) ◽

pp. 879-895 ◽

Author(s):

Mikhail V. Safonov

Keyword(s):

Elliptic Equations ◽

Second Order ◽

Measurable Coefficients ◽

Second Order Elliptic Equations

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Linear Elliptic Equations with Measurable Coefficients

Partial Differential Equations ◽

10.1007/978-0-8176-4552-6_10 ◽

2009 ◽

pp. 297-345

Author(s):

Emmanuele DiBenedetto

Keyword(s):

Elliptic Equations ◽

Measurable Coefficients

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W 1, p(·)-Regularity for Elliptic Equations with Measurable Coefficients in Nonsmooth Domains

Communications in Mathematical Physics ◽

10.1007/s00220-014-1962-8 ◽

2014 ◽

Vol 329 (3) ◽

pp. 937-958 ◽

Author(s):

Sun-Sig Byun ◽

Jihoon Ok ◽

Lihe Wang

Keyword(s):

Elliptic Equations ◽

Measurable Coefficients ◽

Nonsmooth Domains

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A sharp Hölder estimate for elliptic equations in two variables

Proceedings of the Royal Society of Edinburgh Section A Mathematics ◽

10.1017/s0308210500003826 ◽

2005 ◽

Vol 135 (1) ◽

pp. 165-173 ◽

Author(s):

Tonia Ricciardi

Keyword(s):

Elliptic Equations ◽

Type Inequality ◽

Divergence Form ◽

Two Dimensional ◽

Measurable Coefficients ◽

Hölder Estimate

We prove a sharp Hölder estimate for solutions of linear, two-dimensional, divergence-form, elliptic equations with measurable coefficients, such that the matrix of the coefficients is symmetric and has unit determinant. Our result extends some previous work by Piccinini and Spagnolo. The proof relies on a sharp Wirtinger type inequality.

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