Article
MSC:
35J60,
35J65,
35R20,
47H05,
49J40,
73G05,
74A55,
74K20,
74M15,
74S30 | MR 0547039 | Zbl 0479.73041 | DOI: 10.21136/AM.1979.103816
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Keywords:
first and second boundary value problems; at least one W2,2-solution; polar form has no non-trivial kernel; inhomogeneities fulfil certain sign condition; pseudomonotone semicoercive variational inequalities
first and second boundary value problems; at least one W2,2-solution; polar form has no non-trivial kernel; inhomogeneities fulfil certain sign condition; pseudomonotone semicoercive variational inequalities
Summary:
The paper deals with the generalized Signorini problem. The used method of pseudomonotone semicoercive operator inequality is introduced in the paper by O. John. The existence result for smooth domains from the paper by O. John is extended to technically significant "angular" domains. The crucial point of the proof is the estimation of the nonlinear term which appears in the operator form of the problem. The substantial technical difficulties connected with non-smoothness of the boundary are overcome by means of a proper choice of the auxiliary function.
References:
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[2] Jakovlev G. N.: Boundary properties of functions of class $W_p^1$ on domains with angular points. (Russian). DANSSSR, 140 (1961), 73-76. MR 0136988
[3] John O.: On Signorini problem for von Kármán equations. Aplikace matematiky 22 (1977), 52-68. MR 0454337 | Zbl 0387.35030
[4] John O., Nečas J.: On the solvability of von Kármán equations. Aplikace matematiky 20 (1975), 48-62. MR 0380099
[5] Knightly G. H.: An existence theorem for the von Kármán equations. Arch. Rat. Mech. Anal., 27 (1967), 233-242. DOI 10.1007/BF00290614 | MR 0220472 | Zbl 0162.56303
[6] Nečas J.: Les méthodes directes en théorie des équations elliptiques. Academia, Prague 1967. MR 0227584
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