Zobrazeno 1 - 10
of 60
pro vyhledávání: '"Bozhidar Velichkov"'
Autor:
Luca Spolaor, Bozhidar Velichkov
Publikováno v:
Mathematics in Engineering, Vol 3, Iss 1, Pp 1-42 (2021)
We give three different proofs of the log-epiperimetric inequality at singular points for the obstacle problem. In the first, direct proof, we write the competitor explicitly; the second proof is also constructive, but this time the competitor is giv
Externí odkaz:
https://doaj.org/article/905543fcf7da4980aa2885a4b0fd2a92
Autor:
Bozhidar Velichkov
This open access book is an introduction to the regularity theory for free boundary problems. The focus is on the one-phase Bernoulli problem, which is of particular interest as it deeply influenced the development of the modern free boundary regular
Autor:
Bozhidar Velichkov
Publikováno v:
Lecture Notes of the Unione Matematica Italiana ISBN: 9783031132377
Let D be an open set in $$\mathbb {R}^d$$ ℝ d and $$u:D\to \mathbb {R}$$ u : D → ℝ be a (non-negative) local minimizer of $$\mathcal F_\Lambda $$ ℱ Λ in D
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::0c86d503397e3b708e029088f3e85b6b
https://doi.org/10.1007/978-3-031-13238-4_6
https://doi.org/10.1007/978-3-031-13238-4_6
Autor:
Bozhidar Velichkov
Publikováno v:
Lecture Notes of the Unione Matematica Italiana ISBN: 9783031132377
This chapter is dedicated to the regularity of the flat free boundaries. In particular, we will show how the improvement of flatness (proved in previous section) implies the C1, α regularity of the free boundary (see Fig. 8.1). The results of this s
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::61ccc3f4cf77db0dbdd387a05f27e4b6
https://doi.org/10.1007/978-3-031-13238-4_8
https://doi.org/10.1007/978-3-031-13238-4_8
Autor:
Bozhidar Velichkov
Publikováno v:
Lecture Notes of the Unione Matematica Italiana ISBN: 9783031132377
In this chapter, we prove Theorem 1.4. As in the original work of Weiss (see [52]), we will use the so-called Federer’s dimension reduction principle, which first appeared in [32].
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::724b179d56fbe04120b6ec232163f4ed
https://doi.org/10.1007/978-3-031-13238-4_10
https://doi.org/10.1007/978-3-031-13238-4_10
Autor:
Bozhidar Velichkov
Publikováno v:
Lecture Notes of the Unione Matematica Italiana ISBN: 9783031132377
In this section we prove the non-degeneracy of the solutions to the one-phase problem (2.1). Our main result is the following.
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::b8b2a7467445e89111e5d1cd787e0b91
https://doi.org/10.1007/978-3-031-13238-4_4
https://doi.org/10.1007/978-3-031-13238-4_4
Autor:
Bozhidar Velichkov
Publikováno v:
Lecture Notes of the Unione Matematica Italiana ISBN: 9783031132377
In this section, we prove that local minimizers of the functional $$\mathcal F_\Lambda $$ ℱ Λ do exist (Proposition 2.1) and we give several important examples of local minimizers that can be computed explicitly (Proposition 2.10, Lemmas 2.15 and
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::b0155b58756b20794bc26c7214bc86f4
https://doi.org/10.1007/978-3-031-13238-4_2
https://doi.org/10.1007/978-3-031-13238-4_2
Autor:
Bozhidar Velichkov
Publikováno v:
Lecture Notes of the Unione Matematica Italiana ISBN: 9783031132377
The free boundary problems are a special type of boundary value problems, in which the domain, where the PDE is solved, depends on the solution of the boundary value problem.
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::8aae454efc230d29c785fb797651b9f7
https://doi.org/10.1007/978-3-031-13238-4_1
https://doi.org/10.1007/978-3-031-13238-4_1
Autor:
Bozhidar Velichkov
Publikováno v:
Lecture Notes of the Unione Matematica Italiana ISBN: 9783031132377
This chapter is dedicated to the monotonicity formula for the boundary adjusted energy introduced by Weiss in [52]. Precisely, for every Λ ≥ 0 and every u ∈ H1(B1).
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::f70d980732aeba53f26ea6a70fa3711f
https://doi.org/10.1007/978-3-031-13238-4_9
https://doi.org/10.1007/978-3-031-13238-4_9
Autor:
Bozhidar Velichkov
Publikováno v:
Lecture Notes of the Unione Matematica Italiana ISBN: 9783031132377
In this section, we will prove that the local minimizers of $$\mathcal F_\Lambda $$ ℱ Λ are Lipschitz continuous. Our main result is the following.
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::e8f343ed73898bcbb5b2d42b148768c8
https://doi.org/10.1007/978-3-031-13238-4_3
https://doi.org/10.1007/978-3-031-13238-4_3