Regularity properties of solutions to transmission problems

Luis Escauriaza, Jin Keun Seo

Type: Article

Publication Date: 1993-01-01

Citations: 52

DOI: https://doi.org/10.1090/s0002-9947-1993-1149120-8

Abstract

We show that the gradients of solutions to certain elliptic and parabolic transmission problems with internal Lipschitz boundary and constant coefficients at each side of the internal boundary are square integrable along the internal boundary.

Locations

Transactions of the American Mathematical Society - View - PDF

Similar Works

Action	Title	Year	Authors
+ PDF Chat	Regularity Properties of Solutions to Transmission Problems	1993	Luis Escauriaza Jin Keun Seo
+	Regularity for solutions of transmission problems across internal Lipschitz boundary	1991	Jin Keun Seo
+	Transmission problems: regularity theory, interfaces and beyond	2023	Vincenzo Bianca Edgard A. Pimentel José Miguel Urbano
+ PDF Chat	On a regularity theorem for weak solutions to transmission problems with internal Lipschitz boundaries	1992	Luis Escauriaza Eugene B. Fabes Gregory C. Verchota
+ PDF Chat	Interior transmission problems with coefficients of low regularity	2024	Georgi Vodev
+	Regularity ofr Solutions of Transmission Problems for Elliptic Equations with Internal Polygonal Boundary	2011	서진근 금상호
+ PDF Chat	On a Regularity Theorem for Weak Solutions to Transmission Problems with Internal Lipschitz Boundaries	1992	Luis Escauriaza E. B. Fabes G. Verchota
+ PDF Chat	Global Lipschitz continuity for elliptic transmission problems with a boundary intersecting interface	2013	Pierre‐Étienne Druet
+	Regularity of viscosity solutions to fully nonlinear elliptic transmission problems	2022	M. Soria-Carro Pablo Raúl Stinga
+	Interior regularity of solutions of differential equations	1969	Lars Hörmander
+	Interior regularity of solutions of differential equations	1963	Lars Hörmander
+	Interior regularity of solutions of differential equations	1964	Lars Hörmander
+	Interior Regularity of Solutions of Differential Equations	2005	Lars Hörmander
+	Boundary Regularity for Nonlinear Elliptic Systems: Applications to the Transmission Problem	2003	Carsten Ebmeyer Jens Frehse Moritz Kaßmann
+	Global Lipschitz continuity for elliptic transmission problems with a boundary intersecting interface	2010	Pierre‐Étienne Druet
+	Interior transmission problems with coefficients of low regularity	2023	Georgi Vodev
+ PDF Chat	Regularity near the fixed boundary for transmission systems	2024	Alessio Figalli S. Khademloo Sunghan Kim Henrik Shahgholian
+	Optimal regularity for variational solutions of free transmission problems	2022	Diego Moreira Harish Shrivastava
+	A non-isotropic free transmission problem governed by quasi-linear operators	2020	Harish Shrivastava
+	A non-isotropic free transmission problem governed by quasi-linear operators	2020	Harish Shrivastava

Works That Cite This (46)

Action	Title	Year	Authors
+	Shape reconstruction of a conductivity inclusion using the Faber polynomials	2019	Doosung Choi Junbeom Kim Mikyoung Lim
+	Reconstruction of the shape of an inclusion from elastic moment tensors	2011	Mikyoung Lim Sanghyeon Yu
+	Reconstruction of Elastic Inclusions of Small Volume via Dynamic Measurements	2006	Habib Ammari Hyeonbae Kang
+	Sharp Regularity for Elliptic Systems Associated with Transmission Problems	2012	Jingang Xiong Jiguang Bao
+ PDF Chat	Small perturbations of an interface for elastostatic problems	2016	Jihene Lagha Faouzi Triki Habib Zribi
+	Transmission problems and spectral theory for singular integral operators on Lipschitz domains	2004	Luis Escauriaza Marius Mitrea
+	Existence results for a nonlinear transmission problem	2015	Matteo Dalla Riva Gennady Mishuris
+ PDF Chat	Regularity of a transmission problem and periodic homogenization	2021	Jinping Zhuge
+	Identification Problems in Linear Elasticity	1997	Hyunseok Kim Jin Keun Seo
+	Boundary layer techniques for solving the Helmholtz equation in the presence of small inhomogeneities	2004	Habib Ammari Hyeonbae Kang

Works Cited by This (16)

Action	Title	Year	Authors
+	Singular Integrals and Differentiability Properties of Functions.	1971	Elias M. Stein
+	Multiple integrals in the calculus of variations and non linear elliptic systems	1981	Mariano Giaquinta
+	Boundary value problems for the systems of elastostatics in Lipschitz domains	1988	Björn E. J. Dahlberg Carlos E. Kenig Gregory C. Verchota
+	Les Méthodes directes en théorie des équations elliptiques	1967	Jindřich Nečas Jean Dhombres Marie-Ève Maillé Philippe Robba
+	Isolated Singularities of Solutions of Linear Elliptic Equations	1966	James Serrin Hans F. Weinberger
+	Layer potentials and regularity for the Dirichlet problem for Laplace's equation in Lipschitz domains	1984	Gregory C. Verchota
+	L'integrale de Cauchy Definit un Operateur Borne sur L 2 Pour Les Courbes Lipschitziennes	1982	Ronald R. Coifman Alan McIntosh Yves Meyer
+ PDF Chat	Potential techniques for boundary value problems on C1-domains	1978	Eugene B. Fabes Max Jodeit N. M. Rivière
+	The Neumann problem on Lipschitz domains	1981	David Jerison Carlos E. Kenig
+ PDF Chat	On a regularity theorem for weak solutions to transmission problems with internal Lipschitz boundaries	1992	Luis Escauriaza Eugene B. Fabes Gregory C. Verchota