On the solvability of Dirichlet problem for the weighted p-Laplacian

• Autorzy: Dominik Mielczarek , Jerzy Rydlewski , Ewa Szlachtowska
• Języki publikacji: EN

Abstrakty

EN

In this paper we are concerned with the existence and uniqueness of the weak solution for the weighted p-Laplacian. The purpose of this paper is to discuss in some depth the problem of solvability of Dirichlet problem, therefore all proofs are contained in some detail. The main result of the work is the existence and uniqueness of the weak solution for the Dirichlet problem provided that the weights are bounded. Furthermore, under this assumption the solution belongs to the Sobolev space $W₀^{1,p}(Ω)$.

Słowa kluczowe

EN

weighted p-Laplacian; weak solutions; solvability; semi-inner product spaces

Kategorie tematyczne

• 35J20: Variational methods for second-order elliptic equations
• 35A15: Variational methods
• 35J60: Nonlinear elliptic equations

• Wydawca: Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra
• Czasopismo: Discussiones Mathematicae, Differential Inclusions, Control and Optimization
• Rocznik: 2014
• Tom: 34
• Numer: 1
• Strony: 89-103

Daty

wydano

2014

otrzymano

2014-01-31

Twórcy

autor

Dominik Mielczarek

• AGH University of Science and Technology, Faculty of Applied Mathematics, al. Mickiewicza 30, 30-059 Kraków, Poland

autor

Jerzy Rydlewski

• AGH University of Science and Technology, Faculty of Applied Mathematics, al. Mickiewicza 30, 30-059 Kraków, Poland

autor

Ewa Szlachtowska

• AGH University of Science and Technology, Faculty of Applied Mathematics, al. Mickiewicza 30, 30-059 Kraków, Poland

Bibliografia

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Identyfikatory

DOI

10.7151/dmdico1156