Multi-Valued Variational Inequalities in Unbounded Domains

Siegfried Carl; Vy Khoi Le

doi:10.1007/978-3-030-65165-7_6

Multi-Valued Variational Inequalities in Unbounded Domains

Siegfried Carl
, Vy Khoi Le

Mathematics and Statistics

Research output: Chapter in Book/Report/Conference proceeding › Chapter

Abstract

The main focus in this chapter is on multi-valued quasilinear elliptic variational inequalities of the form in all of &reals; N as well as in the exterior domain Ω = &reals; N &ssetmn; B̅(0̅,1̅ ), where only for simplifying our presentation A: X → X &lowast; is given by the p-Laplacian, that is, A = − Δ p , see Section 6.3. The study of elliptic equations in unbounded domains and even more the study of multi-valued quasilinear elliptic variational inequalities in unbounded domains causes a number of additional difficulties, and therefore cannot be considered as just a straightforward extension of the bounded domain problems. That is why the multi-valued lower order term &Fscr; a is of the form &Fscr; a = a&Fscr;(u) with a: &reals; N → &reals; (resp. a: Ω → &reals; ) satisfying a certain decay property at infinity.

Original language	American English
Title of host publication	Springer Monographs in Mathematics
DOIs	https://doi.org/10.1007/978-3-030-65165-7_6
State	Published - Mar 3 2021

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Mathematics
Statistics and Probability

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title = "Multi-Valued Variational Inequalities in Unbounded Domains",

abstract = " The main focus in this chapter is on multi-valued quasilinear elliptic variational inequalities of the form in all of \&reals; N as well as in the exterior domain \Ω = \&reals; N \&ssetmn; B̅(0̅,1̅ ), where only for simplifying our presentation A: X \→ X \&lowast; is given by the p-Laplacian, that is, A = \− \Δ p , see Section 6.3. The study of elliptic equations in unbounded domains and even more the study of multi-valued quasilinear elliptic variational inequalities in unbounded domains causes a number of additional difficulties, and therefore cannot be considered as just a straightforward extension of the bounded domain problems. That is why the multi-valued lower order term \&Fscr; a is of the form \&Fscr; a = a\&Fscr;(u) with a: \&reals; N \→ \&reals; (resp. a: \Ω \→ \&reals; ) satisfying a certain decay property at infinity.",

author = "Siegfried Carl and Le, \{Vy Khoi\}",

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T1 - Multi-Valued Variational Inequalities in Unbounded Domains

AU - Carl, Siegfried

AU - Le, Vy Khoi

PY - 2021/3/3

Y1 - 2021/3/3

N2 - The main focus in this chapter is on multi-valued quasilinear elliptic variational inequalities of the form in all of &reals; N as well as in the exterior domain Ω = &reals; N &ssetmn; B̅(0̅,1̅ ), where only for simplifying our presentation A: X → X &lowast; is given by the p-Laplacian, that is, A = − Δ p , see Section 6.3. The study of elliptic equations in unbounded domains and even more the study of multi-valued quasilinear elliptic variational inequalities in unbounded domains causes a number of additional difficulties, and therefore cannot be considered as just a straightforward extension of the bounded domain problems. That is why the multi-valued lower order term &Fscr; a is of the form &Fscr; a = a&Fscr;(u) with a: &reals; N → &reals; (resp. a: Ω → &reals; ) satisfying a certain decay property at infinity.

AB - The main focus in this chapter is on multi-valued quasilinear elliptic variational inequalities of the form in all of &reals; N as well as in the exterior domain Ω = &reals; N &ssetmn; B̅(0̅,1̅ ), where only for simplifying our presentation A: X → X &lowast; is given by the p-Laplacian, that is, A = − Δ p , see Section 6.3. The study of elliptic equations in unbounded domains and even more the study of multi-valued quasilinear elliptic variational inequalities in unbounded domains causes a number of additional difficulties, and therefore cannot be considered as just a straightforward extension of the bounded domain problems. That is why the multi-valued lower order term &Fscr; a is of the form &Fscr; a = a&Fscr;(u) with a: &reals; N → &reals; (resp. a: Ω → &reals; ) satisfying a certain decay property at infinity.

UR - https://scholarsmine.mst.edu/math_stat_facwork/1033

UR - https://doi.org/10.1007/978-3-030-65165-7_6

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DO - 10.1007/978-3-030-65165-7_6

M3 - Chapter

BT - Springer Monographs in Mathematics

ER -

Multi-Valued Variational Inequalities in Unbounded Domains

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