Solvability in generalized functions of boundary problems for general elliptic systems with a parameter and with discontinuous coefficients

SynopsisLiouville theorems are obtained for general elliptic PDE-systems ℒU(x): = Σlɑl≦21Aα(x) əαU(x)=0 essentially under the assumption that ℒ satisfies a coerciveness estimate over .

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Computational investigation of elliptic systems with discontinuous coefficients

Cybernetics and Systems Analysis ◽

10.1007/bf02667068 ◽

2000 ◽

Vol 36 (4) ◽

pp. 605-609

Author(s):

V. V. Skopetskii ◽

S. I. Lyashko ◽

S. A. Voitsekhovskiib

Keyword(s):

Elliptic Systems ◽

Discontinuous Coefficients ◽

Computational Investigation

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A Green's formula and theorems on isomorphisms for general elliptic boundary-value problems with discontinuous coefficients, without assuming normal boundary conditions and conjugation conditions

Ukrainian Mathematical Journal ◽

10.1007/bf01085904 ◽

1976 ◽

Vol 28 (2) ◽

pp. 147-153

Author(s):

Yu. V. Kostarchuk

Keyword(s):

Boundary Conditions ◽

Boundary Value Problems ◽

Elliptic Boundary ◽

Discontinuous Coefficients ◽

Elliptic Boundary Value Problems ◽

Conjugation Conditions ◽

Elliptic Boundary Value ◽

General Elliptic ◽

Normal Boundary ◽

General Elliptic Boundary

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Pointwise gradient estimates for subquadratic elliptic systems with discontinuous coefficients

Communications on Pure & Applied Analysis ◽

10.3934/cpaa.2019141 ◽

2019 ◽

Vol 18 (6) ◽

pp. 3137-3160

Author(s):

Feng Zhou ◽

◽

Zhenqiu Zhang ◽

Keyword(s):

Elliptic Systems ◽

Discontinuous Coefficients ◽

Gradient Estimates

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HOMEOMORPHISM THEOREMS AND A GREEN'S FORMULA FOR GENERAL ELLIPTIC BOUNDARY PROBLEMS WITH NONNORMAL BOUNDARY CONDITIONS

Mathematics of the USSR-Sbornik ◽

10.1070/sm1970v012n02abeh000916 ◽

1970 ◽

Vol 12 (2) ◽

pp. 177-212 ◽

Cited By ~ 5

Author(s):

Ja A Roĭtberg

Keyword(s):

Boundary Conditions ◽

Elliptic Boundary ◽

Boundary Problems ◽

Green’S Formula ◽

General Elliptic ◽

Green's Formula ◽

General Elliptic Boundary

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The oblique derivative problemfor general elliptic systems in

Research Notes in Mathematics Series - Integral Methods in Science and Engineering ◽

10.1201/9781420036039.ch40 ◽

2000 ◽

Author(s):

Lipschitzdomains Mitrea

Keyword(s):

Elliptic Systems ◽

General Elliptic

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Green matrices and continuity of the weak solutions for the elliptic systems with lower order terms

International Journal of Mathematics ◽

10.1142/s0129167x16500105 ◽

2016 ◽

Vol 27 (02) ◽

pp. 1650010

Author(s):

Jinping Zhuge ◽

Zhenqiu Zhang

Keyword(s):

Bounded Domain ◽

Weak Solutions ◽

Lower Order ◽

Elliptic Systems ◽

Pointwise Estimates ◽

Schauder Estimates ◽

General Elliptic ◽

Method Of Potentials ◽

Type Classes ◽

Lower Order Terms

In this paper, we consider the second-order elliptic systems with lower order terms coefficients belonging to Kato–Stummel type classes in a bounded domain [Formula: see text], where [Formula: see text]. We establish the existence, global pointwise estimates and [Formula: see text] estimates for Green matrices. Based on these estimates, we are able to show the continuity of weak solutions for the general elliptic systems by using method of potentials. We also obtain the optimal Schauder estimates for weak solutions.

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